Preheat the broiler. Arrange the peppers on a baking sheet and broil, turning occasionally, until charred, 8 to 10 minutes. Transfer to a bowl, cover with plastic wrap and let steam 15 minutes. Peel, seed and cut the peppers into 1/3-inch-wide strips. In a medium bowl, toss the peppers with 1 1/2 tbsp. EVOO, the red wine vinegar, 1 tsp. kosher salt and the garlic. Let marinate 30 minutes.
In a large skillet, cook the bacon over medium heat until crispy, about 5 minutes. Transfer the bacon to paper towels to drain. Drizzle 1 tbsp. warm bacon drippings over the peppers; toss to coat.
Fill a large, deep skillet with water. Add the distilled white vinegar and 1/2 tsp. kosher salt; bring to a gentle simmer. Break 1 egg into a small bowl; gently slide the egg into the water. Repeat with the remaining eggs. Cook the eggs, undisturbed, to desired doneness, about 3 minutes for a runny yolk and 5 minutes for a firmer one. Using a slotted spoon, remove the eggs. Transfer to a plate. Season.
In a small bowl, mix the goat cheese, the remaining 3 tbsp. EVOO and 1 tsp. kosher salt. Spread the goat cheese mixture over the ciabatta roll bottoms. Toss the watercress and bacon with the pepper mixture; divide among the ciabatta roll bottoms. Top each sandwich with an egg and a ciabatta roll top.