Preheat the oven to 375 degrees F (190 degrees C).
Place squash halves on a baking sheet. Brush insides with about 1 tablespoon olive oil and season with salt and pepper.
Bake in the preheated oven until squash is tender enough to scoop out and mash, about 30 minutes. Leave oven on.
Place sweet potatoes into 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. Saute until onion has softened and browned, 5 to 7 minutes.
Remove 1/3 of the onion-garlic mixture. Add ground turkey to the skillet with the rest of the onions. Saute until turkey is no longer pink, 5 to 7 minutes. Add turkey gravy, Worcestershire sauce, thyme, and oregano. Cook and stir until flavors combine, 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 together until smooth.
Spread turkey mixture into the bottom of a 9-inch square baking pan. Top with corn and peas; add the sweet potato mash last. Sprinkle with chili powder.
Bake in the hot oven until top begins to brown, 30 to 45 minutes.