1. Preheat oven to 400°F.
2. Make dip: In a small bowl, combine chile, lime juice, and sour cream.
3. Make quesadillas: Arrange squash, onion, and garlic in a single layer on a baking sheet. Drizzle with oil and toss to coat. Roast until garlic is tender. Transfer garlic to a work surface. Roast squash and onion until tender, about 15 minutes. Discard peels from onion and garlic.
4. In a food processor, puree squash, onion, and garlic with black pepper until smooth. Spread a quarter of the puree on each of 4 tortillas. Sprinkle each with a quarter of the bell pepper and a quarter of the cheese.
5. Top each with a plain tortilla, pressing gently together.
6. Coat a griddle with cooking spray. Heat it over medium-high until hot. Cook quesadillas, one at a time, until golden, about 3 minutes per side; transfer to a cutting board. Cut each into 6 to 8 wedges; serve warm with dip. Cook’s note: Both the dip and the squash puree can be made 2 days ahead. Cover and chill.