Preheat oven to 400 degrees F (204 C) and position a rack in the middle of the oven.
Add cubed butternut squash and the UNPEELED garlic cloves to a baking sheet and drizzle with a little olive oil and a pinch each salt and pepper. Toss to combine.
Bake for 15-20 minutes, or until all squash is fork tender and the garlic is golden brown. Let cool 5 minutes.
Peel roasted garlic and add to food processor or blender, along with squash, fresh minced garlic, lemon juice, chickpeas, tahini, olive oil, salt, pepper, parsley, cinnamon, cumin, and smoked paprika (optional).
Purée until creamy and smooth, scraping down sides as needed and adding more olive oil or a touch of water if it's too thick.
Taste and adjust seasonings. Then serve immediately with pita chips and vegetables of choice (see notes for roasted carrots). Alternatively, refrigerate until fully chilled - about 3-4 hours - for a thicker, creamier dip.
Store leftovers, covered, in the refrigerator up to 4-5 days, though best when fresh.
*To roast carrots, preheat oven to 375 degrees F (190 C). Remove greens, peel, and slice any large carrots in half lengthwise. Transfer to a baking sheet and lightly drizzle with olive or grape seed oil and a pinch each salt and pepper. Toss to coat. Then arrange in an even layer and bake for 20-30 minutes or until golden brown and tender. *Recipe as written yields roughly 2 cups hummus.