Make tomato compote using first three ingredients: Heat oil in heavy medium skillet over medium heat. Add tomatoes and sugar. Stir until tomatoes are very tender and mixture is thick, about 15 minutes. Season tomato compote with salt and pepper.

 

Make fish: Melt 2 Tbsp butter in heavy large skillet over medium-high heat. Add mushrooms and chopped shallots. Sauté until liquid evaporates and mushrooms begin to brown, about 8 minutes. Cool completely.

 

Using electric mixer, beat 5 Tbsp butter in large bowl until light. Beat in egg, parsley, 1 Tbsp thyme, 1 tsp salt and 1/2 tsp pepper. Mix in breadcrumbs and mushroom mixture. Preheat oven to 450 degrees F. Sprinkle sliced garlic, sliced shallots and remaining 1 tsp thyme over bottom of 15" x 10 x 2" glass baking dish. Add fish stock, then fish fillets. Sprinkle fish with salt and pepper. Spoon breadcrumb mixture atop fish, covering tops of fish completely and pressing slightly to adhere (can be prepared 8 hours ahead). If prepared ahead of time, cover tomato compote and fish separately, refrigerate and reheat compote over medium-low heat before serving.

 

Bake fish until opaque in center, about 15 minutes. Transfer to broiler. Broil just until topping is crisp and golden, about 1 minute.  Using slotted spatula, transfer fish to plates. Transfer cooking liquid to another medium skillet. Bring cooking liquid to simmer over medium heat. Add remaining 1 Tbsp butter and whisk just until melted and well blended. Season sauce to taste with salt and pepper. Spoon sauce around fish. Spoon dollop of tomato compote alongside and serve fish immediately.