Set a large 2 to 3 gallon stockpot filled with water over high heat and bring to a boil. Immerse the lobsters in the boiling water and cook for 3 minutes. Remove the lobsters from the pot and immediately plunge into an ice water bath. Once the lobsters are cool enough to handle, remove them from the water and place on a clean kitchen towel draped over a cutting board.

Twist the tails off the lobsters, and cut the tails in half using a large chef's knife (score along the length of the tail), remove the meat from the shells. Set the cut tails aside, and crack the shells of the claws to remove the meat. Place the lobster meat aside as you prepare the poaching liquid.

Add the champagne, sliced shallots, 1 teaspoon of garlic, the bay leaf, peppercorns, lemon juice, orange zest, kosher salt, and tarragon sprigs to a 3-quart, straight-sided sauté pan. Bring the contents of the pan to a boil, and reduce to a very low heat (bubbles forming on the bottom of the pan that rise slowly and gently will indicate the proper temperature). Place the lobster meat in the poaching liquid and cook, partially covered, until the meat is cooked through, about 6 to 8 minutes.

Remove the lobster from the pan and chill until ready to serve the salad. Increase the heat to high under the poaching liquid, and bring it to a boil. Cook until the liquid is reduced to 2 tablespoons, about 10 minutes. Strain the poaching liquid through a fine-meshed sieve into a medium-sized mixing bowl and reserve.

Place a small sauté pan over medium heat and add the 2 teaspoons of olive oil. Once the oil is hot, add the minced shallots to the pan and cook until translucent, about 1 minute. Deglaze the pan with the orange juice. Once the juice has almost evaporated, pour the mixture into the bowl with the reduced poaching liquid. Using a whisk, combine the liquid with the shallots and add the mustard, honey, Champagne vinegar, and pepper. Continue whisking vigorously while you slowly drizzle the extra-virgin olive oil into the bowl. Add the caviar and chopped tarragon to the vinaigrette.

Combine the mache salad mix, tomatoes and avocados in a large mixing bowl. Chop the reserved lobster meat into bite-sized pieces and add to the salad. Drizzle about 6 to 8 tablespoons of the dressing over the salad, and toss to combine. Adjust the seasoning with salt and pepper if necessary. Plate the salad on 4 salad plates and serve immediately.