Trim and discard discolored stem ends from mushrooms; thinly slice mushrooms. In a 10- to 12-inch frying pan over high heat, stir mushrooms in 1 tablespoon butter often until lightly browned, 12 to 15 minutes. Spoon into a shallow 1 1/2-quart casserole or divide equally among 4 shallow ramekins (about 1 1/2 cups each).
Add remaining butter and the onion and chilies to pan. Stir often until onion is limp, about 5 minutes. Add flour, mix well, and stir in broth. Purée mixture in a blender or food processor; return to pan. Add sour cream and stir over high heat until boiling. Remove from heat and add lime juice. Rinse fish, arrange in an even layer over mushrooms in casserole (or equally in ramekins), and cover with sauce.
Bake in a 400° oven until fish flakes when prodded, 12 to 15 minutes. Season with salt.
Note: Nutritional analysis is per serving.