Step 1Remove the veins from the foie gras as described in the story. Season the liver generously with all of the pink salt, pepper and sugar. Place the liver in a resealable plastic bag and fill the bag with coarse salt so the liver is completely covered. Refrigerate for 8 to 12 hours. Do not let the liver stand any longer or the foie gras may be excessively salty.
Step 2Rinse off the salt under cold water and pat dry with a towel.
Step 3In a large braising pan, heat the duck fat or canola oil to 160 degrees and submerge the liver in the fat for 30 minutes. Be sure to maintain an even temperature during the cooking process.
Step 4Remove the liver from the fat, and roll it in plastic to form a roulade, or cylinder-like shape. Refrigerate overnight until firm.
Step 1Combine the honey and vinegar in a saucepan and cook over medium-high heat until the mixture reduces to a light syrup, about 8 to 10 minutes.
Step 2Peel and core the apples, and cut them into an even, small dice. People may have different ideas of what makes a "small dice," but what's most important is to make sure they are even in size, or they will not cook evenly.
Step 3Add the apples to the syrup, season to taste with salt and pepper, and cook, stirring frequently, until the apples are tender and the liquid has been absorbed, about 25 minutes. The compote can be cooled and refrigerated until ready to use.
Step 1Reduce the vinegar and honey over medium heat in a small saucepan, just as you did for the compote. Keep an eye on the temperature to keep the syrup from bubbling over. Halfway through the cooking process, add the pepper, and reduce to about 3/4 cup of syrup that is thick enough to coat the back of a metal spoon. This will take about 30 minutes. Remove the pan from the heat from time to time so the bubbles subside and you can check the texture of the sauce. Skim any foam from the top.
Step 1When you are ready to serve the dish, heat the broiler.
Step 2Combine the brioche cubes with the melted butter or foie gras fat. Unroll the liver from the plastic wrap and slice it in 1/2-inch disks. Press the brioche mixture firmly onto the foie gras. Place the liver disks on a baking sheet. Set the sheet about 6 inches beneath the broiler element and broil until golden brown, about 30 seconds. Watch carefully as they scorch easily. Serve with the Apple Compote and Black Pepper Gastrique.