Slice tenderloins into about 1-inch pieces; flatten each medallion with a meat mallet.
In a large skillet over medium heat, melt 1 tablespoon butter with 1 tablespoon oil. Cook mushrooms until tender, about 5 minutes, then add onion and cook for 1 minute longer. Transfer the mushrooms and onions to a plate; set aside. Pour off excess liquids from the pan.
Melt remaining butter with oil over medium heat. Add pork tenderloin medallions and cook for about 3 minutes on each side, or until browned. Sprinkle the pork lightly with salt and pepper. Pour in wine and half of the chicken broth. Reduce heat to low, cover, and cook for 15 minutes. Transfer the pork to a serving dish and keep warm.
Stir flour into the remaining chicken broth until smooth. With the skillet over medium heat, stir in the flour and broth mixture. Cook, stirring, until the sauce is thickened. Taste and add salt and pepper, as needed. Stir in the sour cream, parsley, and the cooked mushrooms and onions. Heat through, but do not boil. Serve sauce with the pork slices.