Preheat the oven to 400°F (200°C) and bring a large pot of generously salted water to a boil for the pasta.
Cook the fettuccine until al dente according to package directions, then drain and set aside.
In a small bowl, combine 2 1/2 tablespoons olive oil with 1/4 tsp salt, 1/4 tsp pepper, 1/4 tsp garlic powder, and 1/4 tsp paprika to make the roast seasoning.
Toss the broccoli with about 2 tablespoons of the seasoning mixture in a large bowl, spread on a baking sheet, and roast for 4 minutes.
Toss the shrimp with the remaining seasoning mixture, then add the shrimp to the baking sheet with the broccoli and roast 6–8 more minutes, until shrimp are opaque and broccoli is crisp-tender.
While the shrimp and broccoli roast, heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-low heat; add the minced garlic and sauté 30 seconds.
Sprinkle in 1/4 cup flour and cook, stirring, about 3 minutes until the raw flour smell is gone, then reduce heat to low.
Slowly whisk in 1 3/4 cups chicken broth and 1 1/2 cups milk until smooth, then increase heat to medium-high and simmer until slightly thickened, stirring occasionally.
Stir in 1 tsp dried basil, 1/2 tsp salt combined with dried parsley and onion powder (total 1/2 tsp), 1/4 tsp black pepper, and a dash of red pepper flakes if using.
Reduce heat to medium-low and stir in 1/2 cup Parmesan, 3/4 cup mozzarella, and 2 oz cubed cream cheese until all cheeses melt and the sauce is smooth.
Add the roasted broccoli and shrimp to the skillet, then add the drained fettuccine and toss until everything is coated in the sauce; add a splash of milk if needed to loosen the sauce.
Taste and adjust seasoning with additional salt, pepper, or red pepper flakes as desired, then garnish with extra grated Parmesan, chopped fresh parsley, and a squeeze of lemon juice if using.
