Place chicken tenders between 2 pieces of plastic wrap and pound with a meat tenderizer to flatten slightly.

Mix together the flour, salt, pepper, and paprika in a shallow bowl. Coat chicken pieces in flour mixture and set aside on a sheet pan until all pieces have been coated.

Melt 2 tablespoons butter and 2 tablespoons olive oil in a large skillet over medium heat. Place half of the chicken in the pan and cook until browned, about 5 minutes per side. Remove chicken to a sheet pan. Heat the remaining butter and oil in the pan, and repeat with the remaining chicken pieces. Set chicken aside.

Combine mushrooms and shallots in the same skillet and cook until the mushrooms release their juices, about 5 minutes. Add garlic and cook for 1 more minute. Transfer mixture to a bowl and set aside.

Bring 2 1/2 cups water to a boil in the same skillet and whisk in beef base until dissolved. Add Madeira wine, bring to a boil, and cook until mixture has reduced by about 1/3. Return mushrooms, shallots, and garlic to the skillet and let simmer.

Mix cornstarch and cold water together in a small bowl. Add to the skillet and boil until sauce thickens slightly, at least 1 minute.

Return chicken to skillet, reduce heat to low, and cook until chicken is no longer pink in the center and the juices run clear, 7 to 10 minutes more. Remove from heat, sprinkle with parsley, and serve.