Adjust oven rack to middle position and heat oven to 400°F. Line a rimmed baking sheet with aluminum foil. Add the drain rig over.
Place the bacon weave on the drainign rig
Bake bacon until crisp, 25 to 35 minutes.
Using two spatulas, transfer bacon, flat bottom side up, to a paper-towel-lined plate to drain. Pour rendered bacon fat into a small bowl and set aside
Once bacon is cooled, use a sharp knife to cut bacon into two equal squares; set aside.
In a small bowl, use a fork to beat eggs until they are just combined but still streaky, about 10 seconds.
In a nonstick skillet, melt butter over medium heat until it starts to foam and sizzle gently.
Pour eggs into skillet, and tilt pan to distribute eggs evenly.
Cook eggs, gently pushing sides of egg toward center, tilting pan to fill any gaps, until eggs are nearly cooked but surface is barely wet, 60 to 90 seconds.
Reduce heat to low and place one slice of cheese in center of eggs. Using a flat spatula, with the cheese as a guide, fold edges of eggs over cheese, creating a square packet.
Place remaining cheese slice on top of eggs, cover, and cook until cheese is melted, about 60 seconds longer.
In now-empty skillet, heat 1 tablespoon reserved bacon fat over medium heat until shimmering.
Place two slices of bread half in pan, and toast, pressing and swirling bread around pan with hand, until bread is golden brown and evenly toasted, 60 to 90 second
Spread mayonnaise, ketchup if using, evenly over both toasted bun halves.
Place bacon squares on bottom bun and top with egg-cheese packet.
Season with salt and pepper to taste. Sprinkle with minced jalapenos if used.