Step 1

Preheat oven to 400°. Place kabocha and delicata squash on separate large rimmed baking sheets. Drizzle with oil; season with salt and pepper. Roast, tossing occasionally, until squashes are golden brown and tender, 30–35 minutes for kabocha and 20–25 minutes for delicata.

Step 2

Meanwhile, bring chiles, vinegar, honey, raisins, red pepper flakes, and a pinch of salt to a boil in a small saucepan over medium heat. Reduce heat and simmer until syrupy, 8–10 minutes.

Step 3

Brush half of warm agrodolce over warm squash. Transfer to a platter.

Step 4

Just before serving, reheat remaining agrodolce, adding a splash of water if needed to loosen. Spoon over squash.

Step 5

Do Ahead: Dish can be made 3 hours ahead. Store tightly wrapped at room temperature.