Preheat 375°. Mix shallots with 1 tablespoon oil and roast in a shallow baking pan in lower third of oven 25 minutes.
Mix together squash, bell peppers, sweet potatoes, salt, cumin, coriander, cinnamon, and remaining 3 tablespoons oil. Add roasted shallots and divide between 2 large shallow baking pans.
Dot vegetables in each pan with half of butter and roast in upper and lower thirds of oven, stirring occasionally and switching position of pans halfway through roasting, until vegetables are tender, about 45 minutes total.