Boil a large pot of salted water. Cook the pasta according to package directions until al dente. Drain, reserving 1/2 cup of pasta water.
In a large skillet over medium-high heat, melt 1 tablespoon of the butter. Add the diced chicken breast, season with salt and pepper, and pan-sear for 6-8 minutes until cooked through. Remove chicken from the skillet and set aside.
Reduce the heat to medium. Add the remaining 3 tablespoons of butter to the skillet. Once melted, stir in the minced garlic, Dijon mustard, lemon juice, smoked paprika, and red pepper flakes. Cook for 1 minute until fragrant.
Whisk the heavy cream into the skillet, scraping up any browned bits from the bottom. Simmer for 3-4 minutes until the sauce slightly thickens.
Stir in the grated Parmesan cheese and the reserved chicken.
Add the cooked pasta to the skillet, tossing well to coat evenly. If the sauce is too thick, add a splash of the reserved pasta water.
Garnish with chopped fresh parsley and serve immediately.