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. (If not using broth: Remove 1¼ 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 broth (or pasta cooking water), ricotta cheese and Parmesan 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 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.