Preheat oven to 375 degrees. Make the filling: Melt butter in a large pot over medium heat. Cook onion until translucent, about 7 minutes. Add fennel, and cook until softened, about 7 minutes. Stir in flour. Add stock and water. Bring to a simmer.
Remove from heat, and stir in lobster, peas, cream, and tarragon. Season with salt and pepper if needed. Let cool. Transfer mixture to a 9-by-12-inch (8-cup) gratin dish.
Make the topping: Melt butter, and brush over bread slices. Tear each slice in half, and arrange over top of filling to cover the surface, overlapping as you work. Bake until bread is golden brown and filling is bubbling, about 30 minutes.
I got my lobsters at Costco
(they are good quality at a cost effective price!)