Bring a large pot of salted water to boil and cook the orzo according to package directions until al dente, usually 8 to 10 minutes. Drain and set aside.

While the pasta cooks, pat the shrimp completely dry with paper towels and season them with salt, pepper, and paprika.

Heat olive oil in a large skillet over medium-high heat. Add the seasoned shrimp in a single layer and cook for 1 to 2 minutes per side until pink and curled. Remove shrimp to a plate.

Reduce heat to medium. Add butter to the same skillet, then add minced garlic and red pepper flakes if using. Cook for 30 seconds until fragrant but not browned.

Add the cooked orzo to the skillet along with lemon zest, lemon juice, and heavy cream if desired. Toss everything together for about 1 minute to coat the pasta.

Add the chopped spinach and stir until just wilted, about 30 seconds.

Return the shrimp to the skillet and gently fold in the Parmesan cheese and fresh parsley. Taste and adjust seasoning with salt and pepper as needed.

Serve immediately while hot, with extra Parmesan and lemon wedges on the side.