Preheat oven to 400°F/205°C. Set aside a casserole dish (ungreased), ideally 13x9-inch, but you can also separate into two smaller dishes.
Cook onions, celery, carrots (optional): If you want your veggies very soft, pre-cook them a little. Add onion, celery, and carrots to a microwave-safe container with a splash of water (I use a Lekue steamer*). Cover and microwave for 2 minutes just to start cooking the veggies.
Blend sauce: Add all sauce ingredients to a blender and blend until smooth.
Mix everything: Add veggies, mushrooms, chickpeas, frozen peas, and pasta to a large mixing bowl. Pour the sauce over and mix until well combined.
Add to casserole dish: Transfer the mixture to your casserole dish(es). Make sure there is still some space at the top since the mixture will bubble. Make sure the pasta is just barely submerged in liquid so it cooks. Cover the dish with foil.
Bake: Place in the middle rack of your oven and bake for 40 minutes or until the pasta is al dente. Tip: If you're able to, after 30 minutes, stir the casserole so the pasta on top gets soaked in the liquid. Remove the foil very carefully and avoid putting your face directly over the dish as there will be a lot of steam. This helps the pasta cook evenly.
Rest: Remove the casserole from the oven and let it rest, covered, for 5-10 minutes. The casserole will be liquidy at first, but the pasta will soak up more liquid as it sits.