Preheat the oven to 350 degrees F.
Heat the oil in a large Dutch oven over high heat until it begins to shimmer. Pat the meat dry on both sides with paper towels and season with salt and pepper. Sear in the oil until golden brown on both sides. Remove to a baking sheet.
Add the onions and carrots to the pot and cook until soft, about 5 minutes. Add the garlic and cook for 1 minute. Add the beer and cook until reduced by half. Return the brisket to the pot and add enough chicken stock to come halfway up the sides. Add the bay, thyme, and parsley and season with salt and pepper. Bring to a boil, cover, and transfer to the oven. Cook until fork tender, about 3 hours. Remove to a baking sheet.
While the brisket is cooking, combine the sugar and vinegar in a medium saucepan, bring to a boil, and cook until thickened and reduced to about 3/4 cup. Let cool slightly.
Preheat the broiler. Brush the top of the brisket with some of the glaze, top with the crushed peppercorns, and broil until the glaze bubbles a bit.
To assemble the sandwiches: Slice the brisket across the grain. Spread some Steak Sauce Mayonnaise on the insides of the hoagie rolls. Pile some brisket on the rolls; if desired, drizzle some extra glaze on top. Top with some scrambled eggs and crushed potato chips.
Whisk together all the ingredients and season with salt and pepper, to taste. Cover and let sit in the refrigerator for at least 1 hour before serving to allow the flavors to meld.
Melt the butter in a large nonstick saute pan over medium heat. Add the eggs and cook until soft peaks form. Fold in the cheese, remove from the heat, and season with salt and pepper.