Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions until al dente. Reserve 1/2 cup of the pasta water before draining and set the pasta aside.

While the pasta cooks, heat the olive oil in a large skillet over medium-high heat. Season the chicken pieces with salt and black pepper. Add to the skillet and cook until golden brown and cooked through, about 6-8 minutes. Remove the chicken and set aside.

In the same skillet, reduce heat to medium and melt the butter. Add the minced garlic and cook for 1 minute until fragrant. Whisk in the Dijon mustard, lemon juice, lemon zest, smoked paprika, red pepper flakes, and cayenne.

Slowly pour in the heavy cream, whisking constantly. Let the mixture simmer gently for 2-3 minutes until it starts to thicken. Stir in the grated Parmesan cheese until melted and smooth.

Add the cooked chicken and drained pasta back to the skillet. Toss to coat everything in the sauce. If the sauce is too thick, add a splash of reserved pasta water.

Stir in the chopped parsley and chives. Toss once more and serve immediately.