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: Add onion, celery, and carrots to a microwave-safe container with a splash of water (I use a Lekue steamer*). Microwave for 2 minutes or until veggies are just cooked.
Blend sauce: Add all sauce ingredients to a blender and blend until smooth.
Mix everything: Add cooked 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.
Stir and continue baking: Carefully remove the foil (be careful of steam - don't put your face directly over the dish) and stir the casserole so the pasta on top gets soaked in the liquid. Return to the oven and bake another 10-20 minutes until all the pasta is tender.
Rest: Remove the casserole from the oven and let it rest, covered, for 10 minutes. The casserole will be liquidy at first, but the sauce will thicken as it sits.