Place the chicken breasts between two sheets of heavy plastic (resealable freezer bags work well) on a solid, level surface. Firmly pound the chicken with the smooth side of a meat mallet to a thickness of about 60mm. Whisk together the flour, paprika, cayenne pepper, salt and black pepper in a shallow bowl. Press each chicken breast into the flour mixture on both sides. Tap off excess flour.
Heat olive oil and 1 tablespoon of butter in a frying pan over medium heat until the butter gives off a slightly toasted fragrance then pan-fry the chicken until browned on both sides, about 3 minutes per side. Set aside. Melt 1 more tablespoon of butter in the frying pan then cook and stir the onion until translucent, about 5 minutes; stir in the shiitake mushrooms, oyster mushrooms, brown mushrooms, garlic then cook until the mushrooms have given off their juice and begun to brown, 10 to 12 minutes.
Fill a large saucepan with lightly salted water and bring to a rolling boil over high heat. Stir in the fettuccine then return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through but is still firm to the bite, about 8 minutes. Drain well. Place the pasta into a serving dish then toss with 2 tablespoons of butter; season to taste with salt and black pepper. Keep warm.
After the mushroom juices have evaporated, pour Marsala wine or sherry into the sauce then scrape up and dissolve any browned flavor bits in the bottom of the frying pan. Turn heat to high then stir until half the wine evaporates, about 3 minutes; stir in mascarpone, Dijon mustard and chicken stock; cook, stirring constantly, until the sauce has thickened slightly, another 3 minutes. Reduce heat to medium-low; return cooked chicken breasts to the sauce. Cook until the chicken juices run clear and the sauce has thickened, about 5 minutes. Stir in parsley. Serve with buttered fettuccine.
Substitute 1/4 cup thickened cream for mascarpone cheese if desired.