Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the homemade pie dough into about a 14-inch circle. Carefully transfer the dough to the lined baking sheet.
Starting in the center of the dough, arrange the sliced tomatoes, mozzarella, and basil in overlapping circles, leaving 2-3 inches of dough exposed around the edges.
Fold the edges of the dough over the filling to create a rustic, pleated crust.
In a medium bowl, whisk together the eggs, heavy whipping cream, salt, and pepper until smooth.
Brush the exposed edges of the dough with the egg mixture. Pour the rest evenly over the tops of the tomatoes, mozzarella, and basil.
Bake for 35-40 minutes, or until the crust is golden brown and the filling is bubbly, but set.
Remove the galette from the oven and let it cool for about 5 minutes.
Slice and serve warm.