Pat the shrimp dry with paper towels, then season them with the kosher salt and freshly ground black pepper.

Heat the olive oil and 1 tablespoon of the butter in a large skillet over medium-high heat. Add the shrimp in a single layer and cook for about 1–2 minutes per side, just until pink and opaque; transfer them to a plate before they are fully cooked.

Reduce the heat to medium and add the remaining 1 tablespoon of butter. Stir in the garlic and cook for 30–60 seconds, until fragrant but not browned.

Pour in the broth and scrape up the browned bits from the bottom of the skillet. Simmer for 2–3 minutes so the broth picks up the skillet flavor.

Add the heavy cream, Italian seasoning, and optional red pepper flakes. Simmer gently for 3–5 minutes, until the sauce is slightly thickened; do not let it boil vigorously.

Lower the heat and stir in the finely grated Parmesan until melted and smooth. Add the lemon juice and stir to combine.

Return the shrimp and any accumulated juices to the skillet. Simmer gently for 1–2 minutes, just until the shrimp are cooked through.

Taste the sauce and adjust the salt, pepper, and lemon juice as needed. Finish with the chopped fresh parsley and serve immediately.