1. Preheat oven to 375°. Put carrots, sweet potatoes, butter, thyme, salt, and pepper in a 9- by 13-in. pan and cover tightly with foil. Bake for 25 minutes. Stir, then cook, covered, until carrots are very tender, about 50 minutes. Stir in green onions and cook until wilted, about 5 minutes.
2. Coarsely mash vegetables in pan.
*For a nondairy kosher version, use extra-virgin olive oil in place of the butter.
Make ahead: Chill airtight up to 1 day; microwave until hot, stirring occasionally.
Note: Nutritional analysis is per 1/2-cup serving.