Preheat the oven to 375 degrees F. Line a sheet pan with parchment paper and set aside.
Unroll the crescent sheet on a clean cutting board.
Mix together the mozzarella, butter, Parmesan, pesto and garlic in small bowl or pitcher until mixed well. Reserve two tablespoons of the mixture and set aside. Spoon the remaining garlic-butter mixture over the crescent dough sheet, spreading to the edges. Starting with one of the long sides, roll the dough tightly, as if you were rolling cinnamon roll dough. Pinch closed and place seam-side down.
Slice the dough into 12 even pieces and transfer them to the lined sheet pan, spacing them evenly. Spoon 1 teaspoon of the remaining garlic butter on top of each roll. Bake until golden, about 12 minutes.