Bring a large pot of salted water to a rolling boil, then add the spaghetti and cook according to package directions until just al dente. Check it a minute or two before the package time suggests for a slight firmness. Reserve about 1 cup of pasta water before draining.

Pat the shrimp dry with paper towels. In a small bowl, combine the smoked paprika, black pepper, and salt, then toss the shrimp gently to coat.

Heat the olive oil in a large skillet over medium-high heat until it shimmers. Working in batches if needed, add the shrimp to the hot oil and let them sit undisturbed for 1.5 to 2 minutes on the first side. Flip each shrimp and cook for another 60 to 90 seconds until cooked through. Transfer the shrimp to a clean plate.

Reduce heat to medium and add the butter to the same skillet. Once melted, add the minced garlic and red pepper flakes, stirring constantly for about 30 to 45 seconds until fragrant and lightly golden.

Pour in the chicken broth and lemon juice, stirring to deglaze the pan. Add about 1/2 cup of reserved pasta water to create a silky sauce. Stir in the lemon zest and let everything bubble gently for a minute.

Add the drained spaghetti directly to the sauce in the skillet, tossing gently to coat. If the sauce seems too thick, add a splash more pasta water. Return the shrimp to the skillet and toss everything together gently.

Divide the pasta among serving bowls. Top each portion with fresh parsley, minced chives, and grated Parmesan cheese. Finish with a crack of fresh black pepper.