Heat oven to 375°F. In a large nonstick skillet, cook sausage over medium-high heat, breaking up meat with a wooden spoon, until cooked through, about 5 minutes. Stir in pumpkin-pie spice; cook 1 minute more. Stir in pumpkin and half-and-half.
Pour 3/4 cup pumpkin sauce into the bottom of a 2-quart baking dish. Place half of the cooked ravioli on the sauce, top with 3/4 cup sauce, and sprinkle with 1/3 cup grated cheese. Place the rest of the ravioli on top, pour remaining sauce over all, and sprinkle with remaining cheese.
Bake 20 minutes, then broil until cheese on top is golden brown.