Three 1-inch strips orange zest, and 2 teaspoons grated orange zest, for garnish
Pepper
8 tablespoons (1 stick) unsalted butter
2 shallots, chopped
2 teaspoons chopped fresh tarragon
Instructions
Combine the flour and 1 teaspoon salt in a food processor and pulse once or twice. Add the eggs and yolks and turn the machine on. Process just until a ball begins to form, about 30 seconds. Add a few drops of water if the dough is dry and grainy; add a tablespoon of flour if the dough sticks to the side of the bowl. Sprinkle the dough with a little flour and cover; let it rest for about 30 minutes. (At this point, you can refrigerate the dough, tightly wrapped in plastic, for up to 24 hours. Let it sit out for 15 minutes before proceeding.)
Bring 4 cups water in a large pot to a boil. Use tongs to put the lobsters in the pot one by one. Let the water return to a boil, then cook until an instant-read thermometer inserted into the tail meat between the body and the tail joint reads 140°F, 5 to 10 minutes. Use tongs to transfer the lobsters to a colander and let cool.
Separate the meat and shell, putting the pieces of shell back in the pot with the cooking water and the meat in a bowl. Twist off the claws and use a nut-cracker to split them and the knuckles. Use a pick to pull out the meat. Twist to separate the tail from the body. Cut through the soft side of the tail with kitchen shears and crack it open to remove the tail meat. Cut through the underside of the front part of the body to extract the meat there. Cut the meat into bite-sized pieces, then pulse in a food processor until finely chopped but not pureed.
Bring the cooking water to a boil, then adjust the heat so it bubbles gently and cook for 15 minutes. Strain through a fine-mesh sieve, gently pressing on the shells to extract as much liquid as possible, and discard the solids. Return the brodo to the pot and add the orange strips and sprinkle with salt and pepper. Cook over medium-low heat, until reduced by half. Taste and adjust the seasoning. Keep warm, or cool and refrigerate for up to a day.
Put 2 tablespoons butter in a medium skillet over medium heat. When it melts, add the shallots and sprinkle with salt and pepper. Cook, stirring occasionally, until the shallots are soft and jammy but have not colored, 5 to 8 minutes. Stir in the tarragon and remove from the heat. Add to the lobster and toss to coat. Taste and adjust the seasoning. Refrigerate until ready to use or up to 1 day, covered.
Set up your pasta machine and sprinkle the work surface lightly with flour. Cut off about one-third of the dough and wrap the rest in plastic or a towel while you work. Roll the dough lightly in the flour and use your hands to flatten it into a rectangle about the width of the rollers. Set the machine to its thickest setting and roll the dough through. If it sticks, dust it with a little more flour. Repeat. Set the machine to its next-thinnest setting and repeat. Each time, if the pasta sticks, sprinkle it with a little more flour, and put the dough through each setting twice.
Continue to roll the dough thinner, changing the thickness only one setting a time (if you try to rush the process, the dough will tear). If at any point the dough tears badly, bunch it together and start again. Use only as much flour as you need to. Pass the dough through the machine’s third-thinnest setting. Repeat 2 more times (by this time it will be going quickly), then flour the dough lightly, and cover. Repeat with the remaining dough.
Put a little water in a small bowl and lightly dust your work surface with flour. Cut the pasta sheets into thirty-two 4- to 5-inch squares. Dip your finger in water and dampen the edges. Drop a heaping tablespoon of the lobster in the center of each square. Fold the dough over onto itself into a triangle, pressing with your fingers to seal. Pick up the triangle and press the 2 bottom corners together around your middle fingers; make sure the top corner folds down and inward, toward the sealed tips.
Put the remaining 6 tablespoons unsalted butter in a small skillet over medium heat. Cook, swirling the pan occasionally until the butter is browned and smells toasted, 3 to 5 minutes. Strain the brown butter through a coffee filter or cheesecloth to remove the solids. Pour the brown butter into the lobster brodo and stir to combine. Remove the orange peel, taste, and adjust the seasoning.
Bring a large pot of water to a boil and salt it. Bring the brodo to a gentle bubble. Add the tortelloni to the boiling water, and cook, stirring occasionally, until they rise to the surface, 2 to 3 minutes. Use a slotted spoon to transfer the pasta to serving bowls. Pour about 1⁄2 cup hot brodo in each bowl, garnish with orange zest, and serve.