Lobster Toasts With Avocado and Espelette Pepper

If using live lobster, bring a large pot of generously salted water to a boil and prepare a large bowl of ice water. Add lobster to boiling water, cover, and cook for 9 minutes, until shell is bright red all over. Drain and transfer lobster to ice water to cool. Remove meat from claws, knuckles, and tail; pat lobster meat dry with paper towels and cut into 1/4" pieces. Combine mayonnaise, crème fraîche, 1 tsp. lemon juice, lemon zest, 1 tsp. tarragon, and chives in a medium bowl. Fold in lobster meat and season with salt. Mash avocado in a small bowl with remaining 1 tsp. lemon juice and season with salt. Meanwhile, preheat oven to 350 °F. Cut brioche into twenty-four 1 1/2" squares. Toast on rimmed baking sheet until lightly browned and dry, about 12 minutes. Spread avocado on toasts and top with lobster salad. Sprinkle with espelette pepper and tarragon and serve.