Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, usually about 1-2 minutes less than the package instructions. Drain well and set aside.
Heat olive oil in a large skillet over medium heat. Add the minced garlic and red pepper flakes, stirring until fragrant, about 1 minute. Add the shrimp, seasoning with salt and pepper, and cook until they turn pink and curl, about 2-3 minutes per side. Remove shrimp from the skillet and set aside.
In the same skillet, pour in the chicken or vegetable broth and lemon juice. Scrape up any brown bits from the bottom of the pan for extra flavor. Let the sauce simmer for 3-4 minutes to reduce slightly.
Return the cooked shrimp to the skillet with the sauce. Add the drained pasta and chopped parsley, stirring gently to combine everything evenly.
Preheat your oven to 375°F (190°C). Transfer the pasta and shrimp mixture into a greased baking dish. Sprinkle the shredded mozzarella and grated Parmesan cheese evenly over the top.
Bake uncovered for 15-20 minutes, or until the cheese is melted, bubbly, and golden brown.
Let the Shrimp Scampi Pasta Bake cool for a few minutes before serving. Garnish with extra parsley or a squeeze of fresh lemon juice if desired, and enjoy!