Step 1

Preheat oven to 425°F. Toss carrots with 2 tablespoons oil and ½ teaspoon salt on a large rimmed baking sheet; arrange in a single layer. Cover with aluminum foil and bake for 15 minutes. Uncover and continue to bake, stirring once, until tender and slightly charred, about 25 minutes.

Step 2

Meanwhile, stir together mayonnaise, 3 tablespoons drained chiles, and ¼ teaspoon garlic powder in a small bowl.

Step 3

Combine pork, cumin, and remaining ¾ teaspoon salt, ½ teaspoon garlic powder, and drained chiles in a medium bowl. Shape into 4 (½-inch thick) patties.

Step 4

Heat remaining 1 tablespoon oil in a large skillet over medium-high. Add patties; cook, flipping once, until browned and cooked through, 3 to 4 minutes per side.

Step 5

Assemble burgers on toasted buns with mayonnaise mixture and arugula. Serve with carrot fries.