Preheat oven to 375°F. Brush a baking sheet with 1 tablespoon olive oil.
Place squash and sweet potatoes on prepared baking sheet, cut side down. Roast until very tender (poke with a fork to test), about 50 minutes.
Cool. Scoop flesh out with a spoon and transfer to large saucepan. Mash with potato masher until smooth.
Stir in broth. Season puree to taste with salt and pepper. (Puree can be made 1 day ahead. Cover and refrigerate.)
Heat oil in heavy large skillet over medium heat. Add onions and poblano (or bell pepper), and sauté until onions are golden brown and tender, about 15 minutes.
Season to taste with salt and pepper. (Can be made a day ahead and refrigerated in a closed container. Bring to room temperature next day).
Bring puree to simmer, adding more broth to thin if necessary.
Stir in 3/4 of onion-bell pepper mixture. Transfer to serving bowl. Top with remaining onion-bell pepper mixture and serve.