Step 1Place the lobsters in a tight-fitting pot. Cover with cold water. Drain off the water and measure it. For every 8 quarts of water, add one-half cup of white distilled vinegar.
Step 2In a separate large pot, bring the vinegar water to a boil. Pour it over the lobsters. Cover the pot, turn off the heat and let steep 2 minutes (for lobsters up to 1 1/2 pounds). Remove the lobsters from the hot water and drain. Discard the water.
Step 3One at a time, using a towel or rubber gloves to hold the hot lobsters, grasp their tails and twist and pull to detach them. Reserve the bodies. Hold each tail flat and twist the tail fan to one side: pull off and discard. Use your fingers to gently push the meat through the tail end and pull the meat out through the large opening at the other end. Reserve the shell. Lay the tail meat on its back and cut lengthwise in half. Remove the vein running through the top of the meat. Place the meat on a paper towel-lined plate or platter, cover with plastic wrap and refrigerate.
Step 1Heat the oil in a large, deep-sided pot. Add the lobster shell pieces and sear over medium-high heat until they turn red, 1 to 2 minutes per side (if your pot is not big enough to hold all the shells, sear them in 2 batches).
Step 2Add the tomatoes, carrots and tarragon, cover the shells and vegetables with water, and bring to a boil. Skim off any impurities that rise to the top. Reduce the heat and simmer over low heat for 1 hour. Strain the stock through a large strainer, smashing the shells with a wooden spoon to extract all the liquid, and then strain again into a clean saucepan.
Step 3Return the strained stock to the stove and simmer until it is reduced to 1 cup. (This may take 1 1/2 to 2 hours, depending on the amount of water added initially.) Add the heavy cream, return to a simmer, and cook, skimming occasionally, until the broth is reduced to 1 1/4 cups, about 1 hour. Strain through a fine strainer into a container, discarding any solids remaining in the strainer. Cover and refrigerate the broth for several hours or up to 3 days.
Step 1Heat the oven to 325 degrees. Line a baking sheet with a silicon nonstick liner. Sprinkle about 2 teaspoons of the cheese on the liner. Use your fingers to spread the cheese into a 2-inch circle. Repeat with the remaining cheese to make 6 rounds. Bake until golden brown, 8 to 10 minutes. Use a small spatula to transfer the rounds to paper towels. They will still be soft when they are removed but will stiffen as they cool. Store in an airtight container for up to 2 days.
Step 1If the lobster pieces have been refrigerated, bring them to room temperature.
Step 2Place the lobster broth in a saucepan and bring it to a simmer.
Step 3Cook the orzo in boiling, lightly salted water until just tender. Drain the cooked pasta in a strainer and rinse under cold water. Shake the strainer to remove excess water and add the orzo to the lobster broth.
Step 4Heat the orzo and lobster broth to a simmer. Add the mascarpone and season with salt to taste. Let simmer for a minute, then remove the pan from the heat and keep warm.
Step 5Melt the butter in a large saucepan and whisk in 1 tablespoon of water. Arrange the lobster pieces in the saucepan in one layer; the lobster should almost be covered. Heat gently on low heat to warm the lobster through, about 8 minutes. Do not let the butter take on any color.
Step 6Stir the chives into the orzo. Place about one-third cup of orzo in the center of a serving plate. Arrange a piece of lobster in the center of the orzo and top each serving with a Parmesan crisp.