Step 1The day before serving the final dish, heat the oven to 350 degrees. Generously butter a 9-by-5-inch loaf pan. Line the bottom of the pan with a sheet of parchment paper that has been folded in half to double its thickness and trimmed to fit the bottom of the pan.
Step 2In a large mixing bowl, beat the eggs, sour cream, milk, Dijon mustard and kosher salt together until homogenous. Add 6 cups of leftover stuffing to this mixture and fold together with a rubber spatula until thoroughly combined.
Step 3Pour the mixture into the loaf pan and gently tap to dislodge any air pockets and to even the surface. Loosely cover the pan with a piece of aluminum foil, taking care not to allow the foil to touch the surface of the food.
Step 4Place in the oven and bake for 1 hour, then remove the aluminum foil covering the pan. Continue to bake until a pairing knife inserted in the center of the loaf comes out clean, about 30 additional minutes. Once done, remove from the oven and set aside to cool on the counter top for about 20 minutes before transferring to a refrigerator overnight.
Step 1The eggs can be poached one day in advance of serving. Fill a stock pot with hot water approximately 6 to 8 inches deep. Add the distilled vinegar and season the water with salt. Bring the water to a low simmer. Carefully crack 2 of the large eggs (for poaching) into a small dish with a tablespoon or so of distilled vinegar in it.
Step 2To begin poaching the eggs, gently swirl the simmering water with a spoon in a clockwise direction. Quickly and gently drop two of the large eggs one by one into the center of the swirling water. Allow to poach to desired doneness, about 3 to 4 minutes. Remove the eggs from water with a slotted spoon and place in a large bowl containing ice water to stop the cooking process. Repeat this process with the remaining eggs until you have 8 poached eggs.
Step 3After the eggs have been chilled, remove them from the ice water and use a pair of scissors to trim away any stringy bits from the eggs. Place the trimmed eggs in a single layer inside an airtight container and refrigerate.
Step 1About one-half hour before you wish to serve the "pain perdu," remove the eggs from the refrigerator and set them aside to come to room temperature. Place a large pot of salted water on the stove and bring to a simmer.
Step 2Make the Gouda sauce: Combine the cornstarch and water in a small dish and mix together until milky and smooth. In a small sauce pot, combine the milk, Dijon mustard and salt. Bring the milk mixture to a simmer on the stove, then add the cornstarch mixture and whisk vigorously until the milk has thickened. Continue to cook for an additional 30 seconds, then add the grated Gouda cheese. Whisk the sauce until the cheese is melted and the mixture is smooth and homogenous. Remove from heat, cover and keep warm.
Step 3Unmold the "pain perdu," using a pairing knife to cut alongside the inner edges of the pan in order to separate it from the pan. Quickly invert the pan over a cutting board and lift the pan away. Remove the parchment paper from the "pain perdu" if it is still attached. Slice the "pain perdu" lengthwise into 4 slices about three-fourths-inch thick, and cut each slice in half to make 8 slices.
Step 4Heat a large nonstick pan over medium heat. Add the butter, and when it is melted and foamy, griddle the "pain perdu." Place the sliced "pain perdu" into the pan and cook it on one side until golden brown, then turn the slices over and cook the other side in the same manner. Remove each cooked slice to a warm plate.
Step 5Immerse the poached eggs in simmering water for about a minute to warm. Remove the eggs with a slotted spoon and drain them on a paper towel. Place one egg on top of each slice of "pain perdu." Spoon the Gouda sauce over the eggs and "pain perdu." Finish by sprinkling the eggs with minced chives and seasoning with cracked pepper. Serve immediately.