In a large skillet, combine mushrooms, broth, onion, thyme and basil. Bring to boiling; reduce heat and boil gently, uncovered, about 20 minutes or till chicken broth has almost evaporated, stirring occasionally. Remove from heat; cool for 10 minutes. Stir in bread crumbs.
Meanwhile, place a chicken breast half between 2 pieces of plastic wrap. Using the flat side of a meat mallet, pound chicken lightly to about 1/4 inch thick. Remove plastic wrap. Repeat with remaining chicken breast halves. Sprinkle chicken breasts lightly with salt and pepper. Evenly spread about 1/4 cup of the filling on each chicken piece. Fold in the bottom and sides; roll up. Press all edges firmly to seal in the filling. Secure with wooden toothpicks.
In a 12-inch oven-going skillet, heat the butter and oil. Add chicken rolls. Cook over medium-high heat about 5 minutes or till golden brown, turning to brown all sides. Bake, uncovered, in a 375 degree F oven for 30 to 35 minutes or till chicken is no longer pink (170 degree F). Remove toothpicks.
Meanwhile, in a small saucepan, stir together marinara sauce and cream; heat through (do not boil). To serve, slice stuffed breasts. Serve with sauce. Makes 6 servings.