Preheat the oven to 350°F (175°C).

In a large pot, bring lightly salted water to a boil. Add the penne and cook, stirring occasionally, until tender but still firm to the bite, about 11 minutes. Drain the pasta and set it aside.

While the pasta is cooking, heat 1 tablespoon of butter and oil in a large oven-safe skillet over medium heat. Add the garlic and cook until fragrant, about 30 seconds. Add the shrimp, 2 tablespoons of parsley, and dill, and cook until the shrimp are bright pink on the outside and opaque on the inside, about 1 ½ to 2 minutes per side. Transfer the shrimp to a plate, leaving the cooking juices in the pan.

Melt the remaining 2 tablespoons of butter in the same skillet over medium heat. Whisk in the flour until fully combined and slightly golden, about 30 seconds to 1 minute. Gradually whisk in the chicken broth, followed by the milk. Stir in the tomatoes, lemon juice, salt, and pepper, and bring to a simmer.

Add ½ cup of Parmesan and Romano cheese, stirring until the cheeses melt and the sauce becomes creamy. Add 1 tablespoon of mozzarella cheese, then mix in half of the cooked pasta. If there’s enough sauce, add the rest of the pasta. Stir in the shrimp, then top with the remaining mozzarella, Parmesan, and parsley.

Bake in the preheated oven until the top is golden and the edges are bubbling, about 8 to 10 minutes.