Place a steamer basket in a large saucepan and add 1 inch of water. Bring to a boil, cover and steam for 3 minutes. Uncover, remove from heat and set aside.
Whisk broth and 2 tsp. flour in a small bowl until smooth. Set aside. Place the remaining 1/4 cup of flour in a shallow dish. Sprinkle chicken with salt and pepper and dredge both sides in the flour, shaking off any excess.
Heat oil in a large skillet over medium heat. Add the chicken and cook until golden brown - 3-4 minutes per side, adjusting heat as needed to prevent scorching. Transfer to a plate and cover to keep warm.
Add shallot, wine and the reserved broth mixture to the pan; cook over medium heat until thickened, about 2 minutes. Reduce heat to medium-low; stir in sour cream, tarragon, lemon juice and the reserved asparagus until combined. Return the chicken to the pan and turn to coat with the sauce. Saute until chicken is cooked through. Sprinkle cheese on top of each piece of chicken, cover and continue cooking until the cheese is melted, about 2 minutes.