Spray a large skillet with non stick cooking spray. Heat the oil and butter over a medium heat.
Season chicken breasts with salt, pepper, and Italian seasoning. Place the flour in a small bowl and dredge chicken on both sides.
Add chicken to the skillet and cook until golden brown on each side, about 5 minutes per side. Transfer to a plate and cover with foil to keep warm.
Bring 4 cups of water to a boil in medium saucepan. Add the asparagus and cook for 3 minutes. Drain and set aside.
Prepare the sauce: Whisk the 2 Tablespoons of flour into the skillet until smooth. Add the chicken broth, garlic, shallot, wine, lemon juice, and sour cream. Cook for 2 minutes, whisking frequently.
Place the chicken and asparagus into the sauce. Cook, uncovered, on low heat for 5 minutes, stirring occasionally.
Sprinkle cheese over the chicken breasts, cover skillet, and cook on low heat until cheese is melted, about 2 minutes.
Transfer to a serving platter.
Makes 2 servings