Pat chicken breast dry. Mix the salt & pepper then sprinkle over both sides of the chicken.
Heat a large skillet over medium-high heat. Add 1 tbs of butter and the oil. Add the chicken breasts and brown well on each side; remove from the pan.
In the same skillet, add the onion and stir to coat with the chicken drippings. Reduce heat to low, cover the pan and let the onion cook for about 5 minutes or until they are limp and slightly brown.
Add the paprika and brown sugar. Stir well. Add the cream and stir to blend.
Add the chicken back to the pan. Cover and cook for 15-20 minutes or until chicken tests done (juices are clear or 170F/85C internal temperature.
While the chicken is cooking, prepare the mushrooms--heat a large skillet over high heat and add the remaining 2 tbs butter. Add the sliced mushrooms and toss to coat with the butter. Continue cooking mushrooms, stirring or tossing frequently until the liquid has evaporated and the mushrooms have browned. Set aside.
Remove the lid from the chicken skillet, increase heat to medium and let the juice reduce 50%--about 5 minutes, then add the mushrooms to the chicken.