Bring a large pot of salted water to a rolling boil and cook the linguine according to package directions until al dente, typically 8-10 minutes. Before draining, use a measuring cup to scoop out 1/2 cup of the starchy pasta water and set it aside. Drain the pasta and set aside.

While the pasta cooks, heat olive oil in a 12-inch skillet over medium-high heat until shimmering. Season chicken pieces generously with salt and pepper, then add to the hot pan in a single layer. Cook for 5-7 minutes, flipping halfway through, until golden brown and no longer pink in the center. Remove chicken to a plate.

Reduce heat to medium and melt butter in the same skillet, scraping up any browned bits with a wooden spoon. Add minced garlic, paprika, and red pepper flakes, stirring constantly for about 1 minute until fragrant but not browned.

Stir in Dijon mustard, lemon juice, lemon zest, and chicken broth. Let the mixture simmer gently for 2 minutes while continuing to scrape the pan bottom to incorporate flavorful browned bits into the sauce.

Pour in heavy cream and half of the chopped parsley, stirring gently. Cook for 2-3 minutes until the sauce thickens slightly and coats the back of a spoon.

Return cooked chicken to the skillet along with drained linguine and Parmesan cheese. Using tongs, toss everything together for 1-2 minutes, adding reserved pasta water 2 tablespoons at a time until sauce reaches desired consistency. The sauce should cling to the pasta without being watery. Taste and adjust seasoning with salt and pepper.

Garnish with remaining fresh parsley and extra Parmesan cheese. Serve hot.