Put oven rack in lower third of oven and preheat oven to 450°F.
Cook garlic in oil in a 12-inch heavy skillet over moderate heat for 1 to 2 minutes, until golden. Add arugula and cook, stirring frequently, until wilted, 2 to 3 minutes. Drain arugula and remove as much water as possible, then coarsely chop.
Stir together ricotta, mozzarella, Parmigiano-Reggiano, yolk, salt, and pepper until blended. Stir arugula into mixture.
Quarter pizza dough, then roll out each piece into an 8-inch round with a rolling pin. Put one fourth of cheese filling (about 1/3 cup) in center of 1 round and fold dough in half to enclose filling and form a semicircle. Press edges together to seal.
Beginning at 1 end and working toward the other, stretch sealed edge outward, pinching and rolling edge to form a rope, and transfer to baking sheet. Make 3 more calzones in same manner, transferring to baking sheet.
Bake calzones until golden and puffed, 12 to 15 minutes. Remove from oven and cool on baking sheet 5 minutes before serving.