Preheat the oven to 400°F (200°C).
Cook the fettuccine in generously salted boiling water until al dente, 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; stir to make the spice oil.
Place 2 tablespoons of the spice oil in a large bowl and toss with the broccoli until coated; spread broccoli in a single layer on a baking sheet and roast for 4 minutes.
Toss the shrimp with the remaining spice oil in the large bowl; after the broccoli has roasted 4 minutes, add the shrimp to the baking sheet and roast both for 6–8 more minutes until the shrimp are opaque and the broccoli is crisp-tender.
Meanwhile, heat 1 tablespoon olive oil and 1 tablespoon butter in a large skillet over medium-low heat.
Add the minced garlic and sauté about 30 seconds until fragrant.
Sprinkle in 1/4 cup flour and cook, stirring, about 3 minutes to remove the raw flour taste, then reduce heat to low.
Slowly whisk in 1 3/4 cups chicken broth, then the 1 1/2 cups milk, whisking until smooth; increase heat to medium-high and bring to a simmer.
Stir in 1 teaspoon dried basil, and the 1/2 teaspoon each of salt, dried parsley, and onion powder plus 1/4 teaspoon black pepper and a dash of red pepper flakes if using; simmer until slightly thickened.
Reduce heat to medium-low and stir in 1/2 cup grated Parmesan until melted, then 3/4 cup shredded mozzarella, then the cubed 2 oz cream cheese until the sauce is smooth.
Add the roasted broccoli and shrimp to the sauce, then add the drained fettuccine and toss until everything is well coated; 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.
Garnish with extra freshly grated Parmesan, chopped fresh parsley, and a squeeze of lemon juice if desired, then serve.