1. In a 10- to 12-inch frying pan over medium heat, cook bacon until brown and crisp, about 15 minutes, turning slices as needed. Drain bacon on towels and discard fat.
2. On each of 4 bread slices, lay 2 bacon slices. Arrange cheese, chilies, and tomatoes equally on bacon; sprinkle lightly with salt. Cover each stack with another slice of bread.
3. In a wide, shallow dish, beat eggs with milk to blend. On a 12-inch nonstick griddle or in a 12-inch nonstick frying pan over medium-high heat, melt half the butter. Meanwhile, one at a time, lay sandwiches in egg mixture; let stand about 15 seconds on each side. Lift out; put on griddle, 2 sandwiches at a time.
4. Brown sandwiches on each side, turning as needed, about 10 minutes. When they are cooked, transfer to a baking sheet and keep warm in a 200° oven. Add remaining butter to pan and cook remaining 2 sandwiches. Set hot sandwiches on plates and tuck a lettuce leaf alongside each.