1. Heat charcoal or gas grill to medium. Gently combine ground pork, 1/4 cup beer, sage, poultry seasoning, black pepper and cayenne in bowl. Shape into 6 (1-inch thick) burgers. Grill burgers about 5 minutes per side until internal temperature reaches 160°F.
2. Meanwhile, sauté onion slices in oil over medium heat until very tender and golden brown. Add remaining 1/4 cup beer and continue cooking until liquid is evaporated.
3. Place 1 hash brown patty on bottom of each toasted bagel; top with slice of cheese. Layer burger, fried egg and onions on top of the cheese. If desired, sprinkle with hot sauce; close sandwich to serve.