Place bacon in a 12-inch nonstick skillet. Cook over medium heat 16 to 22 minutes or until crisp, turning often. Drain bacon on paper towels; set aside. Spread 3 tablespoons butter on one side of bread slices. Place 4 bread slices, butter sides down, in small rimmed baking pan. Top each with 1 slice cheese. Drizzle with sriracha, if desired.

Divide and form ham into 4 mounds. Place ham on bread slices with cheese and Sriracha; set aside.

For egg patties, whisk together eggs, water, salt, and pepper in a medium bowl. Heat remaining 1 tablespoon butter in same skillet over medium heat. Pour in egg mixture; gently stir with a silicone spatula until egg mixture begins to set. Stop stirring; sprinkle with chives. Use spatula to carefully lift the cooked edge of egg mixture; tilt skillet so uncooked egg mixture can flow underneath. Cook 1 to 2 minutes or until set. Transfer egg patty to a cutting board and cut into fourths. Place on top of ham on bread slices. Top with bacon, and remaining 4 cheese slices and 4 bread slices with butter sides up. Cover with foil. Refrigerate until ready to grill.

To grill, preheat a charcoal or gas grill for direct cooking over medium-low heat (325°). Remove foil from baking pan. Place pan on grill rack. Grill 5 to 7 minutes or until sandwiches are toasted and cheese is melted, turning once halfway through.