Remove pizza dough from the refrigerator and let it come to room temperature for 90 minutes.
Preheat the oven with a pizza stone on the middle rack for at least 30 minutes to 450°F–500°F (use 500°F if available).
Make the black bean-corn salsa: in a medium bowl combine 3/4 cup black beans (rinsed), 3/4 cup corn, 1/4 cup finely chopped red onion, 1/2 tablespoon olive oil, 2 tablespoons salsa, and 1/4 teaspoon ground cumin; mix and refrigerate until needed.
Make the cilantro-lime cream: in a small bowl stir together 1/3 cup sour cream, 1 tablespoon lime juice, and 2 tablespoons finely chopped cilantro; refrigerate.
Divide the dough into two equal pieces. Working with one piece at a time, stretch or roll into an approximately 12-inch round using your hands or a rolling pin.
Lightly dust a pizza peel or the back of a cookie sheet with cornmeal or flour and place the shaped dough on it to prevent sticking.
Mix 1 cup mild thick-and-chunky salsa with the 2 minced chipotle peppers; spread about 1/3 to 1/2 cup of this sauce over the dough, leaving a small border for the crust.
Top the sauce with half of the shredded Mexican cheese, about 3/4 cup of the diced cooked chicken, and 1/4 cup thinly sliced red onion.
Slide the pizza from the peel onto the hot pizza stone (tilt and shake the peel until the pizza transfers) and bake 5–10 minutes, until the cheese is melted and the crust is golden.
Remove the pizza and top with the black bean-corn salsa, then drizzle with the cilantro-lime cream; repeat the assembly and baking steps for the second pizza.
