Prepare grill for medium heat. Place the bacon slices and peppers on grill. Cook peppers until soft and charred, turning occasionally, 10 to 15 minutes. Cook bacon until brown, turning occasionally and moving to avoid flare-ups, about 10 minutes.
Dice 1 slice of bacon and place in a medium bowl. Dice peppers, add to bowl, and stir to mix. Squeeze the lemon juice over pepper and bacon mixture. Season with 1/2 tsp. salt and 1 tbsp. oil. Add chives and stir, then set salsa aside.
Place a large skillet on the grill. Add remaining oil and the shallots and cook 3 minutes. Add tomatoes, paprika, and remaining salt and cook, stirring occasionally, until mixture is reduced by one-quarter, about 20 minutes. Crack eggs evenly throughout tomato mixture. Sprinkle feta on top. Cook until eggs are cooked through, about
5 minutes. Top with remaining bacon slices, and serve with salsa and bread.