Fill a large saucepan with water, add a generous pinch of salt, and bring to a boil. Cook the pasta following the package guidelines until al dente. Drain well, reserving approximately half a cup of the starchy cooking water.

In a wide skillet set over medium heat, combine the butter with the olive oil. Once melted and hot, arrange the shrimp in a single layer. Season lightly with salt and pepper. Sauté for 1 to 2 minutes on each side until the shrimp are opaque and just cooked through. Transfer to a separate plate.

Using the same pan, add the minced garlic and sauté briefly for about 30 seconds, just until aromatic.

Stir in the heavy cream and chicken broth (or reserved pasta water). Add the grated Parmesan, Italian seasoning, and red pepper flakes. Allow the mixture to gently simmer for 3 to 4 minutes, stirring occasionally, until the sauce begins to thicken.

Return the drained pasta and seared shrimp to the skillet. Gently toss everything together until coated evenly in the cream sauce. If the mixture appears too thick, stir in a splash of reserved pasta water to loosen it to your preferred consistency.

Finish by sprinkling over the chopped parsley and, if desired, a little more grated Parmesan. Serve the dish hot, directly from the pan or plated individually.