Heat 1 tablespoon olive oil with 2 tablespoons butter in a large oven-safe skillet set over medium-high heat.
Season chicken cutlets with Italian seasoning, sweet paprika, onion powder, salt, and pepper.
Add chicken cutlets to the skillet; cook for 4 to 5 minutes per side, or until cooked through and internal temperature registers at 165˚F. Use an Instant Read Meat Thermometer to check for doneness.
Transfer chicken to a plate and keep covered.
Return skillet to medium-high heat and melt 1 tablespoon butter.
Add mushrooms to the skillet; season with salt, and cook for 4 to 5 minutes, or until soft.
Stir in minced garlic and continue to cook and stir for 30 seconds.
Transfer mushrooms to a plate; set aside and keep covered.
Return skillet over medium-high heat.
To the skillet add the wine and stir all the browned bits from the bottom of the pan.
Bring to a boil; continue to boil for 5 minutes.
Whisk in chicken broth; bring to a boil. Continue to cook for 10 more minutes, or until sauce is reduced.
Reduce heat to medium and whisk in the cream.
Let simmer for 1 to 2 minutes, or until sauce thickens.
Taste sauce for salt and pepper; adjust accordingly.
In the meantime, set your BROILER to HIGH.
Return chicken, mushrooms, and asparagus to the skillet.
Sprinkle tops with shredded cheese.
Broil for 3 minutes, or until cheese is melted.
Remove from oven; garnish with parsley and serve.