Melt 6 tablespoons butter in a large pot over medium heat. Add onions, garlic, and salt; cook and stir until onions soften, about 5 minutes. Add lobster shells, mushrooms, apple, red bell pepper, carrots, and tomato paste. Cook and stir until vegetables soften, about 7 minutes. Add water, paprika, curry, tarragon, chili powder, and cayenne pepper. Simmer soup over medium-low heat, uncovered, stirring occasionally, about 2 hours.
Remove soup from heat; strain liquid through a mesh colander into a bowl to yield about 2 quarts. Discard lobster shells and vegetables. Rinse the pot.
Melt remaining 4 tablespoons butter in the pot over medium heat. Add flour; mix vigorously into a thick roux, scraping the bottom of the pot, 2 to 3 minutes. Add the strained liquid, 2 cups at a time, mixing well until entirely smooth, about 5 minutes. Stir in heavy cream, maintaining a low simmer. Divide lobster meat evenly into serving bowls; ladle hot soup generously on top.
