Preheat the oven to 350ºF.

Fill a medium saucepan with water, then add the distilled vinegar. Bring to a boil, then reduce to a simmer. Crack both eggs individually into small bowls.

Dip a large ladle into the simmering water to warm it, then pour most (but not all) of the water out. Add an egg to the ladle and slowly lower it into the water. Hold it there until the white begins to set. Gently lay the egg into the water and swirl the water. Let cook until the white is fully set.

Using a slotted spoon, transfer the poached egg to a paper towel to drain and set aside. Repeat the process with the remaining egg.

Cut the brioche into large cubes and toss in a bowl with olive oil and salt to taste. Bake until golden brown, about 10 minutes. Set the croutons aside to cool.

In a large sauté pan, heat a drizzle of olive oil over medium heat. Add the lardons and sauté until crispy and cooked through. Add the shallot and sauté until soft. Add the sherry vinegar and Dijon mustard, scraping the crispy bits off the bottom of the pan. Turn off the heat.

In a large bowl, combine the frisée, parsley, most of the chives (save some for garnishing), and a few of the croutons. Top with the warm lardon dressing, leaving most of the lardons in the pan for garnishing. Toss to coat.

Transfer the frisée salad to serving plates and top with the remaining lardons, croutons, and chives. Finish with the poached eggs, seasoning them with salt and pepper to taste, and serve.