Place the carrots, onions, and garlic on a half or quarter baking sheet. Drizzle with olive oil and salt and toss to coat. Roast until the vegetables are tender and golden brown, about 24-26 minutes.
Meanwhile, bring a large pot of salted water to a boil over high heat. Cook the pasta according to package directions. Remove 1 cup of the pasta cooking water and set aside to reserve. Drain the pasta, and return it to the pot.
Transfer the roasted vegetables to a blender with the ricotta cheese. Blend until smooth and creamy, adding as much of the pasta cooking water (or broth, if using) as needed to make a smooth sauce.
Add as much of the sauce to the cooked pasta as you like and toss to coat.
Serve immediately with grated Parmesan cheese, and/or black pepper as you like.
Notes
Make the sauce up to 5 days ahead of time and store in an airtight container in the refrigerator. Or, you can freeze it for up to a year in a small freezer container.
Store leftover pasta and sauce in an airtight container in the fridge and reheat as you like.
Dairy-free: Use an equal amount of drained and rinsed white beans in place of the ricotta cheese.