Heat lightly salted water in a large saucepan over medium-high heat until boiling. Add pasta and cook 8 - 10 minutes or until al dente; drain and set aside.
TO MAKE THE ROASTED BROCCOLI AND GARLIC
Preheat oven to 425 degrees F.
Place the broccoli, garlic, olive oil, salt, and pepper in a large bowl. Toss well. Spread out onto large baking sheet. Bake for 20 minutes. Remove from oven and set aside.
TO MAKE THE SAUCE
Melt 2 tablespoons butter in a large skillet over medium heat. Whisk in 2 tablespoons flour and cook for 2 minutes. Slowly whisk in milk and cream,stirring constantly for 5 - 6 minutes until thickened. Stir in the thyme, rosemary, Parmesan cheese, salt, and pepper. Reduce heat to low and keep sauce warm until ready to serve.
TO COOK THE SHRIMP
Melt 1 tablespoon butter in a large skillet over medium heat. Add shrimp and saute for 2 - 3 minutes. Add salt and pepper, cooking and stirring occasionally, another 2 - 3 minutes, or until shrimp are pink and cooked through.
Combine pasta, shrimp, and broccoli in a large bowl. Toss with sauce until evenly covered. Season with salt and pepper, if needed. Garnish with 2 tablespoons Parmesan cheese.