Arrange a rack in the lower third of the oven and place an inverted rimmed baking sheet or pizza stone on it.

In a medium bowl, whisk together the sour cream, mayonnaise, dried dill, dill pickle juice, garlic powder, salt, and pepper. Taste and adjust seasonings as needed.

Take one ball of dough and flatten it with your hands on a lightly floured work surface. Starting at the center and working outwards, use your fingertips to press the dough into a 12 to 14-inch circle. You can also hold up the edges of the dough with your fingers, letting it hang and stretch while working around the edges. Repeat with the second ball of dough.

Lightly sprinkle a pizza peel or rimless baking sheet with cornmeal. Transfer one prepared dough round to the peel. Spoon on half the sauce (about 1/4 cup plus 2 tablespoons) and spread it in an even layer using the back of a spoon, leaving 1/2-inch from the edge bare. Arrange 1/2 cup pickles over the sauce, followed by 1 cup mozzarella cheese and 1/4 cup Parmesan cheese. Top with 1/2 cup pickles and 1/2 teaspoon dried dill.

Carefully sprinkle some cornmeal onto the preheated baking sheet or stone. Slide the pizza onto the sheet (it’s okay if it’s hanging over the edges slightly) and bake for 11 to 13 minutes, until the crust is golden brown and the cheese is bubbling.

Use a pizza peel to remove the pizza from the oven and transfer it to a cooling rack.

Prepare and bake the other pizza in the same manner.