Baked Pasta Shells with Sausage and Greens

Place racks in middle and upper third of oven; preheat to 325°F. Heat a large, deep ovenproof skillet over medium-high. Pour in ¼ cup oil; add sausage and break up into small pieces. Cook, undisturbed, until browned underneath, about 4 minutes. Stir a few times; cook, undisturbed, until cooked through, about 3 minutes.
Add garlic, chopped sage, and red pepper flakes to sausage and cook, stirring, until garlic is golden, about 2 minutes. Mix in half-and-half and simmer until thickened slightly, about 2 minutes. Reduce heat to low. Stirring constantly, gradually add two-thirds of the cheese a little at a time, letting it melt before adding more. Cook, stirring, until sauce is smooth and thick, about 3 minutes; season with salt. Remove from heat.
Meanwhile, cook pasta in a pot of boiling salted water, stirring occasionally and adding broccoli rabe during the last 2 minutes, until very al dente, about 2 minutes less than package directions. Drain in a colander, shaking well. Return pasta and broccoli rabe to pot.
Add sausage mixture to pasta and toss to coat; transfer to skillet. Cover with foil and bake on middle rack until pasta is al dente and sauce is bubbling, 30–40 minutes. Remove from oven. Heat broiler.
Top pasta with remaining cheese. Toss sage leaves and remaining 1 Tbsp. oil in a small bowl; arrange over pasta. Broil on upper rack until cheese is browned in spots, about 5 minutes. Let cool slightly before serving.