If you don't have scallop shells, you can use 4 1/2-inch round broilerproof baking dishes that are 1 inch deep.
Make the stock: Heat oil in a large stockpot over medium heat. Add lobster bodies, and cook, stirring, 10 minutes. Add onion and fennel; cook 15 minutes. Add Cognac; cook, scraping up browned bits with a wooden spoon, until liquid is almost gone, about 1 minute.
Stir in tomato paste; cook 1 minute. Add flour; cook 1 minute. Stir in tomatoes, then cover with 1 inch water. Bring to a boil, then reduce heat. Cover, and simmer until some liquid evaporates and mixture thickens, about 1 hour. Pour stock through a fine sieve into a bowl; discard solids. Return to pot; cook until stock is reduced to 1 3/4 cups, about 15 minutes. Whisk in cream, and simmer until thickened, about 6 minutes.
Make the roux: Melt butter in a saucepan over medium heat. Whisk in flour. Cook until toasty, about 1 minute. Whisk in stock. Bring to a boil. Reduce heat; simmer until sauce is thick enough to coat the back of a spoon, about 5 minutes (you should have about 1 1/2 cups).
Make the potatoes: Place potatoes in a medium pot; cover with 1 inch salted water. Bring to a boil. Reduce heat, and simmer until potatoes are very tender, about 15 minutes. Drain. While potatoes are still warm, pass through a ricer into a bowl. Stir in butter. Add milk, season with salt and pepper, and stir.
Make the vegetables: Heat oil in a medium skillet. Add celery stalks and carrots; cook over medium-high heat 5 minutes. Add celery root, 1 teaspoon salt, and 1/4 teaspoon pepper. Cover, and cook until vegetables are tender, about 10 minutes.
To assemble, preheat broiler. Place 12 scallop shells on a rimmed baking sheet. Place 2 tablespoons vegetable mixture in center of each, and top each with 1/4 cup crabmeat. Spoon 2 tablespoons sauce over top of each. Fill a pastry bag fitted with a 3/4-inch star tip (such as Ateco #88) with potatoes. Pipe rosettes around edges and one in center. Broil until browned on top and bubbling, about 4 minutes. Serve immediately.