Step 1Heat the oven to 500 degrees.
Step 2Roll the pineapple in the coriander, crushed peppercorns and 2 teaspoons of salt. Set aside.
Step 3Cut off a small piece from the end of one of the livers. Cook it over low heat in an ovenproof skillet until all the fat is rendered, about 10 minutes. Discard the foie gras piece. Place the pineapple in the fat and cook over medium heat until golden brown and fork tender, about 6 to 7 minutes, being sure to brown all sides.
Step 4Transfer the skillet to the oven and roast the pineapple for 10 minutes, turning the pieces once halfway through cooking time. Cut each piece into 4 pieces and set aside.
Step 5Cut the foie gras into 8 pieces. Season with salt and pepper. Heat 2 medium cast-iron skillets over high heat until almost smoking. Place 2 pieces of the foie gras in each skillet. Turn off the heat. Sear the foie gras for 30 seconds on each side. (The skillets should be hot enough to sear the foie gras with the heat off.) Transfer the skillets to the oven (still at 500 degrees) and cook until a small sharp knife inserted into the center feels warm to the touch, 6 to 7 minutes. The center of the foie gras should be custard-like with a crisp exterior. Remove the foie gras from the skillets and keep warm. Repeat with the remaining foie gras.
Step 6Reheat the pineapple in one of the same skillets over medium heat, just until warmed through, about 2 or 3 minutes.
Step 7To assemble, place 1 piece of foie gras and 1 piece of roasted pineapple on each of 8 plates. Drizzle each plate with about 2 teaspoons of the gastrique.
Step 1Sprinkle the sugar evenly over the bottom of a medium skillet. Heat the sugar over medium-high heat, swirling the pan as the sugar begins to melt. Do not stir. The caramel should be a deep golden brown in about 8 to 10 minutes. Add the vinegar carefully; it will bubble up. Stir constantly to make sure the caramel dissolves again evenly. Cook over medium heat until the mixture is reduced by half, about 6 to 8 minutes. Stir in the peppercorns. (This makes about 1 cup; you'll have some left over for another use.)