Preheat the oven to 475°F. Line a baking sheet with parchment paper. (See Kelly’s Notes.)
Lightly flour your work surface then roll the dough until it is 1/4-inch thick.
In a medium bowl, stir together the butter, mayonnaise, chives, garlic and black pepper. Once the mixture is smooth, stir in the mozzarella cheese and Parmesan cheese.
Transfer the pizza dough to the prepared baking sheet then spread the cheese mixture on top, leaving a 1-inch border around the edges.
Bake the pizza for 10 minutes then switch the oven to “broil.” Broil the pizza (about 3 inches away from the flame) until it is golden brown and the cheese is bubbling, 3 to 5 minutes.
Remove the pizza from the oven and let it cool slightly before topping with additional chives, then slicing and serving.