It is important to know, that the heat capacity of the pizza will change during the baking process, because water is leaving the system due to evaporation. Therefore we may restrict the calculation to the initial state when the heat capacity is maximal. I would go and deal with this in the following, experimental way:
What you want to know is the heat capacity per mass.
Mass is defined as volume times density.
$$ m = V \cdot \rho $$
Volume is defined for a pizza as area times thickness. We assume, that pieces that are higher like paprika bits and areas that are only covered with sauce and cheese will average each other out and result in a averaged thickness $t_{avg}$.
$$ m = \pi r^{2} t_{avg} \cdot \rho $$
If you want to have precise values for the volume instead of using an approximation value for the thickness, one could freeze the pizza, put it into water and immediately measure the volume increase in a closed container of the water after complete submergence. Alternatively the application of a thin polymer coating at the whole surface area of the pizza could be tried to avoid melting during the measurement.
In our case, the density of an averaged size pizza is unknown and it is needed to be determined by external measurement of dimension and weight. Assuming, we would go with a margarita pizza of 26 cm in diameter and 2 cm in thickness and a weight of 350 g, a density would be calculated as the following:
$$ \frac{0,350 kg}{0,13m^2 \cdot \pi \cdot 0,02m} = 329,79 \approx 330 \frac{kg}{m^3} $$
With that value we can determine the mass of any pizza with similar density and surface structure in dependence of the radius:
$$ m= 330 \frac{kg}{m^3} \cdot \frac{d}{2}^2 \cdot \pi \cdot 0,02m $$
For the next step you would need to determine the heat capacity in a calorimeter. Before this step, the complete pizza would be homogenized with a device like a blender until it is absolute homogeneous.
A predefined mass, for example 30 g of the slurry would be placed into the measurement cell without any remaining air (with a different heat capacity). In a simple calorimeter a well defined amount of heating energy is applied and the temperature change is being measured. The heat capacity of a system is defined as:
$$ C = \frac{dQ}{dT} $$
For a homogeneous pizza slurry:
$$ C = m \cdot c $$
$c$ is the specific heat capacity which is a material constant.
We assume, our calorimeter is applying 480 J of heating energy for a temperature increase of 5 K during the experiment. We use the simplification, that the specific heat capacity of pizza slurry may not be a function of the temperature and is constant. With this information we can calculate the heat capacity of the pizza per mass. Still, we have to consider the instrumental constant of heat capacity for the calorimeter.
$$ C_{Sys}=C_{pizza}+C_{cal} $$
$$ C_{Sys}=c_{pizza} \cdot m_{pizza} + c_{cal} \cdot m_{cal} $$
$$ \frac{c_{sys}-c_{cal} \cdot m_{cal}} {m_{pizza}}=c_{pizza} $$
We assume for the calorimeter, that the heat capacity is only determined by the measurement cell which has a weight of 10 g and a specific heat capacity of $0,42 \frac{J}{gK}$ (common value for steel). Under real life conditions one would need to determine the heat capacity of the calorimeter by own experiments, for example by the application of a defined amount of heating energy to the water filled calorimeter and the subsequent measurement of the temperature of the water, another approach would compare the expected temperature of a resulting water body after mixing two exactly measured volumes of water with defined temperatures (the discrepancy would be caused by the calorimeter). For the sake of the argument we may stick here to the simplification.
Therefore examplaric we receive:
$$ \frac{\frac{480J}{5K} - 2,1 \frac{J}{5K g} 10 g}{30g}=3,06 \frac{J}{gK} $$
Therefore we can set up the final relation between the diameter of an averaged margarita pizza and its heat capacity. One may replace the numeric values with the results of individual experiments.
$$ C_{pizza}=c_{pizza} \cdot \frac{d}{2}^2 \cdot \pi \cdot t_{avg} \cdot \rho $$
$$ C_{pizza}=\frac{c_{sys}-c_{cal} \cdot m_{cal}}{m_{pizza}} \cdot \frac{d}{2}^2 \cdot \pi \cdot t_{avg} \cdot \rho $$
