1. Preheat broiler.
2. In a (12-inch) skillet, bring a 2-inch layer of water (about 4 cups) to a low boil with vinegar. Break an egg into a bubbling area so the bubbles spin the egg and set the white around the yolks. Add remaining eggs, then turn down the heat and poach them so they scarcely bubble for 3 minutes or until desired degree of doneness. To test them, lift an egg with a slotted spoon and press with your fingertip: The white should be set with the yolk still soft. Transfer the eggs to a bowl of warm water. Trim strings from edges of each egg with kitchen shears, if desired.
3. Spread 1 1/2 teaspoons butter over each bread slice. Place bread slices in a single layer on a heavy baking sheet; broil 3 minutes or until golden. Place one toasted bread slice on each of 4 plates; top each serving with 1/2 cup arugula and one egg. Sprinkle evenly with salt and pepper, and serve immediately.