Preheat the oven to 500°F.
Arrange a rack in the lower third of the oven and place an inverted rimmed baking sheet or pizza stone on it to preheat.
In a medium bowl, whisk together the sour cream, mayonnaise, dried dill, pickle juice, garlic powder, salt, and pepper until smooth. Taste and adjust seasonings if needed.
Lightly flour your work surface then flatten one ball of dough with your hands, then press it from the center outward into a 12 to 14-inch circle. You can also stretch it by holding up the edges and letting gravity help. Repeat with the second ball of dough.
Sprinkle cornmeal onto a pizza peel or rimless baking sheet and transfer one dough round onto it.
Spoon on half of the garlic-dill sauce (about 1/4 cup plus 2 tablespoons) and spread evenly, leaving a 1/2-inch border.
Top with 1 cup of mozzarella, 1/4 cup Parmesan, 1 cup pickle slices, and 1/2 teaspoon dried dill.
Sprinkle a little cornmeal onto the hot stone or baking sheet in the oven, then carefully slide the pizza onto it.
Bake for 11 to 13 minutes, or until the crust is golden and the cheese is bubbling.
Use a pizza peel to transfer the pizza to a cooling rack.
Repeat the same process to assemble and bake the second pizza.
Slice and serve warm.