Heat the olive oil in a large pot on medium high until shimmering.
Pulse the mushrooms in two batches in a food processor 7-10 times or until the pieces are on average 1/4" in size
Use a silicone spatula to get all the mushrooms out of the processor bowl into the pot. Season the mushrooms liberally with salt, then cook at medium high for 8 minutes until browned and fragrant.
While the mushrooms cook, repeat the processing pulsing process separately with each of the chickpeas, onions, olives.
Stir the onions into the pot, cook for 5 minutes, stirring occasionally until onions are soft and fragrant
Add the peppers, garlic, Italian seasoning and red peppers flake and cook another 2-3 minutes
Add the tomato paste and chickpeas and cook another 2 minutes, stirring constantly until it turns dark red.
Stir in the passata and vegetable broth, bring to a boil then reduce to a low simmer, cover and cook on low for 10 minutes
Stir the broccoli into the sauce, bring back to a boil, reduce to a low simmer and cover for 10-15 minutes or until the broccoli is fork tender
Cook the bow ties in heavily salter water until almost al dente. Drain the pasta, reserving 1-2 cups of pasta water
Stir the drained pasta into the sauce, then adjust the consistency with the pasta water. Slowly stir in the water until the sauce easily coats all pasta, and clings to the pasta on a fork.
Cover the pasta and simmer another 1-2 minutes or until pasta is al dente