In a 12-inch skillet over moderate heat, melt the butter.
Add the garlic and sauté, stirring occasionally, until translucent, about 1 minute. Add the cream, shrimp, and broccoli and bring to a simmer. Continue cooking, stirring occasionally, until the shrimp is firm and the broccoli is crisp-tender, about 3 minutes. Add the pasta and stir to coat in the sauce. Sprinkle the cheese over the pasta, toss again, and season to taste with salt and pepper. Serve in warm, shallow bowls.