Special equipment: a piece of cheesecloth
For the lobster and shrimp stock with cooked lobster and shrimp: Tie together the peppercorns, garlic, thyme and bay leaf in a piece of cheesecloth for a bouquet garnis.
Bring a large pot of water to a boil. Add the lobster and cook for 6 minutes. Shock in an ice bath to stop the cooking. Remove the lobster from its shell and reserve both the meat and the shell.
Smash the lobster shell with a mallet until crushed into smaller pieces. In a separate large pot, add the lobster and shrimp shells. Pan roast the shells over medium-high heat until the shells become pink/red and are fragrant. Add the leek, onion and enough water to cover (about 2 quarts). Bring to a boil, skim any scum that rises to the surface, add the bouquet garnis and reduce to a simmer. Simmer for 30 minutes or up to an hour over low heat.
Strain the stock through a fine mesh strainer and return it to the pot. Bring to a simmer and reduce the stock by one-third. Lower the heat to low for a slow gentle simmer. Add the shrimp and poach until pink, about 2 minutes. Remove with a slotted spoon, let cool. Chop the shrimp and set aside.
Meanwhile, dice the lobster into small dice and set aside. Measure out 1 cup (5 ounces) chopped shrimp and 1 cup (5 ounces) chopped lobster to combine with the mac and cheese and reserve. Refrigerate any leftover stock, lobster and shrimp in sealed containers for another use. The stock can also be frozen.
For the mac and cheese: Preheat the oven to 375 degrees F.
Bring a 6-quart pot of water to a boil. Cook the pasta according to the package directions. Drain well and transfer to a bowl. Add the Cheddar and 1/2 cup lobster and shrimp stock while the pasta is still hot and toss to coat.
In a separate bowl, combine the milk, sour cream, mustard, eggs, salt and cayenne and whisk together. Combine with the pasta and transfer to a 1 1/2-quart casserole dish sprayed with olive oil cooking spray. Bake until the mixture begins to thicken and set slightly, 15 to 20 minutes.
Gently fold in the reserved 1 cup lobster and 1 cup shrimp meat. Return to the oven and cook until set, another 10 minutes.
In a small bowl, mash together the avocado, lemon juice and a pinch of salt until somewhat smooth.
For the sandwich: Spread 1/8 the avocado mixture on 2 slices toasted bread (about 1 tablespoon per slice of bread). To one of the slices, add a lettuce leaf, a slice of tomato, 1/2 cup of the lobster mac and cheese, the bacon and sprouts. Top with the second piece of bread. Repeat with remaining ingredients for 4 sandwiches.