For the caramelized onions: Melt bacon fat in a large heavy-bottomed pot over medium heat. Add onions and cook slowly, stirring often, until they turn brown, about 20 minutes.
Add salt, pepper and vinegar. Spread out on a cookie sheet and allow to cool.
For the tarragon aioli: Combine the mayonnaise, tarragon, lemon juice and salt in a mixing bowl. Whisk thoroughly until evenly mixed.
For the cheese stuffing: Melt American cheese and Taleggio together in a double boiler. Remove from heat and fold in lemon juice, herbs and lobster meat. Season to taste with salt and pepper. Spread on a cookie sheet to cool and thicken. (Cheese layer should be 1/2-inch thick.)
For the lobster Lucy: Weigh beef out into 3.5-ounce balls. Flatten meatballs into circular patties using wax paper and a 6-inch pizza pan. (Patties should be no more than 1/2-inch thick.) Cut out circles of cheese stuffing using a 1-inch ring mold. (Cheese should be 1.5-ounce pieces.) Place cheese stuffing in center of a beef patty. Place a second beef patty on top of cheese stuffing. Using thumb and forefinger, crimp the two patties all the way around to mold them together, leaving no air inside and no seams in the beef. Repeat with remaining beef and cheese stuffing.
Sprinkle lobster Lucy patty generously with salt and pepper. Heat a frying pan over medium-high heat, add oil and lay patties in pan. Cook for 4 minutes on each side, uncovered and unpressed. Poke a hole in top of each patty after flipping it to allow air pressure out. Allow to rest off heat 2 minutes before serving.
Toast hamburger buns. Place lobster Lucy patties on bottom burger bun. Top each with 1.5 ounces caramelized onions and 1 ounce lobster claw. Spread 1 ounce tarragon aioli on top bun and place over lobster Lucy to finish. Garnish with chopped chives.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.