Preheat the broiler. In a large, deep skillet, heat the EVOO, 3 turns of the pan, over medium-high heat. Add the carrots, celery, shallots and mushrooms and cook until tender, 7 to 8 minutes. Add the shrimp and cook, stirring a few times, until pink and almost firm, about 4 minutes; season with salt and pepper. Stir in the white wine, tomato sauce and tarragon and heat through for 1 to 2 minutes; remove from the heat.
Toast the bread slices under the broiler, rub with the garlic and drizzle with EVOO. Serve the shrimp and sauce in shallow bowls with hunks of the bread for mopping.