Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with olive oil or nonstick spray.

Bring a large pot of salted water to a rolling boil. Cook the spaghetti or linguine until al dente according to package directions, then drain and set aside.

Meanwhile, in a large skillet over medium heat, melt 2 tablespoons of the butter with 2 tablespoons of the olive oil. Add the shrimp and cook for 2 to 3 minutes until they turn pink and just firm. Transfer to a plate.

In the same skillet, add the remaining 2 tablespoons butter and 2 tablespoons olive oil. Sauté the garlic for about 1 minute, until fragrant. Pour in the chicken broth mixture and simmer 2 to 3 minutes, scraping up any browned bits.

Stir in the cream, lemon zest, and lemon juice. Whisk in the Parmesan cheese until the sauce is smooth. Season with salt, pepper, and red pepper flakes if desired.

In a large bowl, toss the pasta, shrimp, and sauce together until evenly coated.

Pour the mixture into the prepared baking dish and spread it out evenly.

Sprinkle the shredded mozzarella over the top.

Bake for 30 to 35 minutes, until the cheese is golden and bubbly.

Let the dish rest for 10 to 15 minutes before serving, so the cheese sets slightly.