Bring a large pot of salted water to a boil over high heat. Add linguine and cook until al dente, typically around 8-10 minutes. Reserve ½ cup of pasta water before draining.

In a large skillet, heat olive oil over medium-high heat. Add chicken, season with salt and pepper, and cook for 5-7 minutes until golden and cooked through. Remove and set aside.

In the same skillet, reduce heat and add butter. Once melted, add garlic, paprika, and optional red pepper flakes; sauté for 1 minute until fragrant.

Add Dijon mustard, lemon juice and zest, and chicken broth; stir well, scraping any browned bits. Simmer for 2 minutes.

Pour in heavy cream and half of the parsley, stirring continuously as the sauce thickens for about 2 minutes.

Return chicken to skillet, add drained linguine and Parmesan cheese (if using). Toss to coat in creamy sauce, adding reserved pasta water if too thick.

Taste and adjust seasoning with salt and pepper, garnish with remaining parsley and more Parmesan if desired. Serve immediately.