First thing to know is that either the object projecting the shadow or the shadow itself have nothing to do with the formation of the effect. As we shall see below, the fact that the shadow is always at the center of the circle is a result that the light rays are backscattered in the direction of the observer.
The glory is not a full circle rainbow. A full circle rainbow also is centered at the shadow of the observer however its angular diameter is $84^\circ$ whereas the angular diameter of the glory is less than $20^\circ$. Unlikely the rainbow the glory cannot be explained just in terms of geometrical optics. There are of course reflections and refraction playing a role but there is also a big role played by diffraction.
The first attempt to an explanation was given by Fraunhofer who suggested the light coming from the Sun is diffracted by foremost droplets in the cloud (those near the head of the observer) and then simply reflected by the inner portions of the cloud (those ahead of the observer). The net result would be a reversed optical corona. However this cannot be true since there are fundamental differences between the glory and the corona, such as the light intensity distribution (as shown by B.B. Ray in 1923) and the light polarization of the rings. Ray tried to apply only geometrical optics but even considering multiple reflections he could not be able to explain the glories since the intensity of the backscattered light would be too small.
In 1947 van de Hulst proposed a mechanism that might explain glories. I basically explains how a plane incident wavefront is transformed into a curved wavefront after emerging the droplet. The figure below show an incident plane wavefront $a$ refracting, reflecting and emerging a droplet as a curved wavefront $b$. The latter has a virtual focus point F, which by axial symmetry turns out to be a ring. Therefore the backscattered light emerges as a toroidal wavefront. Van de Hulst proposed that that the glory emerges as an interference pattern of these toroidal wavefronts.
As well as for the corona, the angular size of the glory depends on the size of the droplets in the atmosphere (order of few microns) as well as the composition of these droplets. Therefore, glories can be used to determine atmospheric properties of other planetes.
The major issue with Van de Hulst's explanation is that the refraction index of water (around $1,33$) is not large enough to result in a backscattering. There is $14^\circ$ missing as can bee seen in the left of the figure below. The red line is the actual path of the ray and the black line is a impossible backscattered path.
Van de Hulst suggested that this $14^\circ$ missing could be overcame if the wave travels in the surface of the droplet in the regions nearby the reflections (both external and internal reflections) as indicates the right figure above. The problem with this idea is that these surface waves decay exponentially and by losing too much energy, the backscattered ray would be too weak.
Philip Laven proposed a mechanism to explain the interference pattern. Light waves penetrating the same droplet would go through different paths (as surface waves) along the the droplet and be backscattered with a different phase originating a series of maxima and minima.
In the late 20th century Nussenzveig et al. proposed that classical tunneling could energetically reinforce the waves traveling in the droplet. The evanescent field of a wave close but outside to the droplet would couple with the wave traveling inside and therefore transfer energy to it. This tunneling effect is possible since the size of the droplet is compared to the wavelength (and therefore it does now happen in rain droplets) and would be the "drive force" for the emerging wave. Note that in his model it is not necessary to assume the surface waves.
Nussenzveig et al. did quantitative studies comparing the three possible effects originating glories and found that the backscattering as proposed by Ray is insignificant and the the main contributions are therefore the Van de Hulst surface waves and his tunneling wave, the latter being the most dominant. According to him, glories are a macroscopic effect of classical light tunneling.
It seems that up to now there is no full understanding about the glory formation. Nussenzveig himself found this new description based on tunneling when trying to find a simpler theory given that the ones available are too complex. Maybe the present knowledge is still complicated and is hidden some more basic concepts. Apparently people are still working on the subject.
References:
http://www.atoptics.co.uk/droplets/glory.htm
http://www.philiplaven.com/Publications/AO-44-27-p5675.pdf
https://www.scientificamerican.com/article/the-science-of-the-glory/
Nussenzveig, Diffraction effects in semiclassical scattering, Cambridge University Press, 1992.
