Step 1Kill the lobsters by making a cut just behind the head. Remove the claws and tails. Put the tails and claws in a large bowl and cover with boiling water. Blanch the claws for 2 1/2 minutes and the tails for 3 minutes. Remove them from the boiling water and shock them in ice water until chilled. (These can be cooked ahead of time, then brought to room temperature when ready to use.)
Step 2Remove the meat from the tails and cut on the bias into 3 or 4 medallions. Remove the meat from the claws and knuckle and set aside. Clean the body shells, removing the innards and scraping the gills. Reserve the shells to make stock for the cream sauce.
Step 1Blanch the carrots, zucchini, potatoes and onions in boiling water until they are almost tender; do not cook them all the way because they will finish cooking in the pie when it is baked. The carrots will need 6 to 8 minutes, the zucchini 2 to 3 minutes, the potatoes about 8 minutes, the onions 2 to 3 minutes.
Step 2Peel the onions and place them in a small skillet with the broth or water and the sugar. Cook over medium heat until the liquid is reduced and the onions are tender and start to brown from the sugar caramelizing, 10 to 15 minutes.
Step 3Meanwhile, lightly sear the mushrooms in the butter in a small skillet over high heat until they begin to color, 2 to 3 minutes. Season with salt and pepper and add to the onions. Add the carrots, zucchini and potatoes and set aside.
Step 1Sift the flour into the bowl of a mixer. With the mixer on low speed, drop the butter into the flour, a few chunks at a time. Season the mixture with salt. Add the water slowly just until dough forms; do not overmix. Shape the dough into 2 disks and refrigerate for 1 hour.
Step 1Place the flour in a saucepan and whisk in the truffle butter over medium heat to make a roux, cooking until the raw flour taste is gone and the mixture smells nutty, about 6 to 7 minutes.
Step 2Sear the lobster shell pieces in the vegetable oil in a skillet over high heat until they turn red, 3 to 4 minutes. Add the onions, reduce the heat to medium and cook until tender, 8 to 10 minutes. Add the tomato paste and cook 5 minutes. Add the brandy and wine to the pan and cook, scraping up any browned bits, until no liquid remains in the pan. Add the cream, shallots, bay leaf, coriander seeds and peppercorns. Bring to a simmer and cook until the liquid is reduced by half, 30 minutes.
Step 3Strain the mixture, discarding the solids, and place the liquid in a saucepan. Whisk in the truffle roux and cook over medium-high heat until the mixture thickens, about 2 to 3 minutes.
Step 1Heat the oven to 375 degrees.
Step 2To assemble, divide the spinach in half and arrange it on the bottom of 2 (3-cup to 1-quart) baking dishes. Divide the reserved vegetables and add to the dishes. Arrange the lobster on top of the vegetables by crossing the claws over the tail. Divide the Truffle Mushroom Cream Sauce and pour over the vegetables and lobster.
Step 3Roll the pie dough out so it is slightly thicker than 1/8 inch and place it on top of each dish. Trim the dough so that it is about 1/2 inch wider than the dish and seal or flute the edges. Brush the tops with the beaten egg and cut 2 to 3 slits in the top of each pie.
Step 4Bake the pies until heated through and the tops are browned, 45 to 50 minutes. Serve immediately.