Slice peppers and onion into large pieces and place on a lined or greased baking sheet. Add garlic and drained and rinsed canned chickpeas. Toss with olive oil. Roast in an oven preheated to 350F for 30 minutes, flipping once halfway through.
When there’s about 30 minutes remaining, bring a large pot of water to a boil. Cook pasta al dente according to package instructions. Once cooked, drain the pasta, reserving at least ¼ cup of pasta water. Add drained pasta back to pot.
When the veggies are done cooking, remove the skin and seeds. Transfer peppers, onion, garlic, and chickpeas to a blender with dairy free milk, dried oregano, salt, and pepper. Blend until smooth. You may need to add extra dairy free milk.
Stir the sauce into the cooked pasta, adding reserved pasta water 1 tablespoon at a time until the desired consistency is reached. Serve warm, topped with fresh basil.