2 pounds medium carrots, scrubbed
2 tablespoons plus 1/4 cup vegetable oil
1 small shallot, thinly sliced
2 red Thai chiles, sliced
1 1/2-inch piece ginger, peeled, thinly sliced
2 garlic cloves, thinly sliced
2 tablespoons fish sauce
2 tablespoons sugar
2 tablespoons fresh lime juice
1 tablespoon mayonnaise
Preheat oven to 425°. Toss carrots and 2 Tbsp. oil on a large rimmed baking sheet and season with salt. Roast, tossing occasionally, until crisp-tender, 20–25 minutes.
Meanwhile, bring shallot, chiles, ginger, garlic, fish sauce, sugar, and 2 Tbsp. water to a gentle simmer in a small saucepan over medium heat and cook just until aromatics are soft, 8–10 minutes (you don’t want the liquid to reduce much). Let cool. Transfer to a blender, add lime juice and mayonnaise, and blend until smooth. With motor running, gradually stream in remaining ¼ cup oil; blend until emulsified. Season dressing with salt.
Drizzle dressing over carrots just before serving.
Do Ahead: Dressing can be made 3 days ahead. Cover and chill.