Bring a large pot of salted water to a rolling boil. Cook pasta according to package directions until al dente, about 8-10 minutes. Before draining, reserve 1/2 cup of pasta water, then drain and set pasta aside.

In a large skillet, heat 1 tablespoon of olive oil and 1 tablespoon of butter over medium-high heat. Season chicken breast with salt, pepper, and paprika; sear until golden brown and cooked through, about 5-7 minutes each side. Transfer chicken to a plate to keep warm.

In the same skillet, reduce heat to medium and add remaining 3 tablespoons of butter. Once melted, add minced garlic and sauté for 1 minute until fragrant and golden.

Pour reserved pasta water into the skillet, bring to a simmer and cook for 2-3 minutes to reduce slightly. Add cooked pasta and seared chicken, tossing gently to coat everything in garlic butter sauce.

Stir in grated Parmesan cheese until melted for creamy texture. Adjust seasoning with more salt and pepper if desired. Fold in freshly chopped parsley and allow to cook for another minute before serving.

Serve warm, garnished with extra Parmesan, chili flakes, and a squeeze of lemon juice if desired, alongside garlic bread or a salad.