Preheat the oven to 375 degrees F (190 degrees C). Place squash halves on a baking sheet. Brush insides with oil and season with salt and pepper. Bake until squash is very tender, about 30 minutes.

Place potatoes in a large pot and cover with water. Bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain.

Heat 1 tablespoon oil in a skillet over medium-high heat. Stir in onion and garlic. Season with salt and pepper. Sauté until onion is soft and brown, 5 to 7 minutes.

Remove 1/3 of the onion-garlic mixture and set aside. Add turkey to the skillet and sauté until no longer pink, 5 to 7 minutes. Add gravy, Worcestershire sauce, thyme, and oregano. Cook, stirring until well combined, 2 to 3 minutes.

Remove and discard squash seeds and scoop insides into a bowl. Add sweet potatoes, reserved onion-garlic mixture, butter, and milk. Mash until smooth.

Spread turkey mixture into the bottom of a 9-inch square baking pan. Top with corn and peas. Spread potatoes evenly over top. Sprinkle with chili powder.