Step 1. Preheat the oven to 425°F (220°C) and line a large baking sheet with parchment paper.
Step 2. Toss the delicata squash with 2 tbsp of the olive oil, half the salt, and half the pepper on the baking sheet, spreading into a single layer.
Step 3. Roast for about 25 minutes, until tender and golden at the edges, flipping halfway through.
Step 4. While the squash roasts, heat the remaining olive oil in a large skillet over medium-high heat. Add the mushrooms in a single layer and cook undisturbed for about 5 minutes, until browned.
Step 5. Stir in the garlic and remaining salt and pepper, and cook for about 3 minutes, until the mushrooms are fully tender and any liquid has evaporated.
Step 6. Push the mushrooms to one side of the skillet (or use a separate small pan). Add the butter and sage leaves, swirling for about 2–3 minutes until the butter turns golden brown and fragrant and the sage crisps slightly.
Step 7. Deglaze by pouring in the balsamic vinegar, stirring to combine with the mushrooms and brown butter, scraping up any browned bits, about 1 minute.
Step 8. Arrange the roasted squash on a serving platter, spoon the mushroom mixture over top, and scatter with toasted pecans and dried cranberries.
Step 9. Garnish with crumbled goat cheese or feta if using, and serve warm.