1. Combine shallots, oil, 1 tablespoon vinegar, mustard, salt, and pepper, stirring with a whisk. Heat a grill pan over medium-high heat. Lightly coat both sides of each bread slice with cooking spray. Add bread to grill pan; cook 3 minutes on each side or until toasted.
2. Add water to a large skillet, filling two-thirds full; bring to a boil. Reduce heat to medium; add remaining 2 tablespoons vinegar to pan. Break eggs into custard cups. When water cools to a simmer, gently pour eggs into pan; cook 3 minutes or until desired degree of doneness. Carefully remove eggs from pan using a slotted spoon.
3. Place 2 toast slices on each of 4 plates. Add arugula to oil mixture; toss. Arrange about 1 cup arugula mixture on each serving; sprinkle evenly with bacon. Top each serving with 1 egg. Serve immediately.