1Melt 2 tablespoons butter in a skillet over medium heat; cook and stir chanterelles in hot butter until tender, 5 to 8 minutes. Transfer chanterelles to a bowl. Melt remaining 7 tablespoons butter in the same skillet and reduce heat to low. Cook butter until it turns pale brown and gives off a nutty fragrance, about 5 minutes.
2Stir tomato and balsamic vinegar into browned butter; cook and stir until tomato is soft, about 2 minutes. Stir cooked tomato and browned butter into mushrooms.
3Set oven rack about 6 inches from the heat source and preheat the oven's broiler.
4Place scallops onto a broiler pan and broil in oven until just opaque, about 2 minutes per side. Serve scallops on a platter topped with chanterelles and sauce.
Footnotes
Cook's Notes:
To serve this as a first course, use sea scallops. Spoon a mound of champ (mashed potatoes with spring or green onions) in center of plate and arrange scallops around. Top with chanterelles.