Bring cream to a very low simmer over medium heat; cook, stirring occasionally, until reduced somewhat and slightly thickened. Stir in cheese and keep warm.

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 shrimp and broccoli and bring to a simmer. Cover and continue cooking, stirring occasionally, until the shrimp is firm and the broccoli is crisp-tender, about 3 minutes. Add the cream sauce and pasta and stir to coat in the sauce. Season to taste with salt and pepper. Serve in warm, shallow bowls.