Pat the chicken dry with paper towels. Season both sides with paprika, part of the salt, and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and sear for 4 to 5 minutes per side, until lightly golden. The chicken does not need to be fully cooked yet. Transfer to a plate and keep any juices.
In the same skillet, add the chopped onion and cook for 3 to 4 minutes, stirring often, until softened and lightly golden.
Add the butter and minced garlic. Stir for about 30 seconds to 1 minute, just until the garlic is fragrant.
Add the sliced mushrooms and cook for 6 to 8 minutes, until they release their moisture, soften, and start to brown lightly.
Sprinkle the flour over the mushrooms and stir well to coat everything evenly. Cook for about 1 minute to remove the raw flour taste.
Slowly pour in the chicken broth while stirring and scraping the bottom of the skillet. Stir in the Dijon mustard, Worcestershire sauce, Italian seasoning, and remaining salt if needed.
Return the chicken and any juices from the plate to the skillet. Spoon some of the mushroom gravy over the chicken.
Reduce the heat to low or medium-low and simmer gently for 8 to 10 minutes, or until the chicken is fully cooked and the gravy has thickened.
Taste and adjust the seasoning if needed. Sprinkle with fresh parsley and serve warm with mashed potatoes, rice, or noodles.