How to Make It
Preheat oven to 425°F. Line a baking sheet with foil. Place carrots on sheet, drizzle with 2 Tbsp. oil, and sprinkle with 1/2 tsp. each salt and pepper; toss. Roast until browned, about 30 minutes, stirring occasionally. Let cool slightly.
In a bowl, whisk balsamic vinegar, shallot and mustard. Whisk in remaining 1/4 cup oil. Place arugula, almonds, Parmesan and carrots in a bowl. Toss with dressing; divide among 4 plates.
Bring 2 inches of water to a boil in a deep skillet. Reduce to a simmer over medium heat. Add white vinegar. Crack 1 egg into a teacup; slide into water; repeat with remaining eggs. Cook until whites are set, about 4 minutes; transfer to salads. Season with salt and pepper. Serve immediately.