Place a pizza stone on the middle oven rack and preheat to 500˚ F. Place a baking sheet on top of the pizza stone.
Warm the olive oil in a small skillet or saucepan over medium heat. Add the sage, red pepper flakes and garlic. Remove from the heat and let cool slightly; season with salt.
Divide the sausage into 16 small balls. Cook in a medium nonstick skillet over medium heat, stirring occasionally, until browned and cooked through, 8 to 10 minutes. Remove to a paper towel–lined plate to drain.
Divide the dough into 16 balls (about 2 inches each). Flatten and shape each into a 3 1/2-inch round on a lightly floured surface. Put 1 piece of cooked sausage in the center of each round and top each with a few cubes of cheese. Very lightly brush the edges of the dough with water. Bring the edges of the dough toward the center, lightly pleating to form a tight package; pinch to seal. Turn seam-side down; using a metal skewer dipped in flour, make a hole in the center of each dough ball to create a steam vent.
Remove the hot baking sheet from the oven and carefully line with parchment paper; place the dough balls on the baking sheet, spacing them 2 inches apart. Brush liberally with the sage oil. Transfer the baking sheet to the pizza stone and bake 5 minutes, then rotate the pan and bake until the rolls are golden brown, about 10 more minutes. Remove from the oven and brush with more sage oil. Sprinkle with the parsley and serve immediately with the remaining sage oil for dipping.