Prepare the crispy chickpeas. Rinse the chickpeas, pat them dry and place them on a parchment-lined baking sheet. Drizzle with a teaspoon of olive oil, season with salt and pepper, and put in the oven at 400° for 15 minutes or in an air fryer for 13 minutes. Stir or shake halfway through. Chickpeas should be crispy and lightly browned; if they need more time, give it to them. When they are done, set them aside.
Mis en place the vegetables. While the chickpeas cook, sliver the onions, quarter the brussels and the mushrooms, and thinly slice the garlic.
Cook the pasta according to package instructions until al dente. Drain, reserving 2 cups of the pasta water.
Caramelize the Vegetables. While the pasta cooks, put a heavy bottomed skillet over medium heat. Melt the butter and add 2 T of olive oil. Add the onions and sauté for a couple of minutes, then add the brussels and the mushrooms and continue to sauté for another 3-4 minutes. Add the garlic and cook and stir for another 2-3 minutes. Season with salt and pepper and add the sugar. Continue cooking until the veggies are brown and caramelized.
Add the pasta to the vegetable mixture along with 1 cup of the reserved pasta water, the lemon juice, the red pepper flakes, and the capers. Stir to combine. Add the cheese and continue to stir. Add additional pasta water as desired. Taste and adjust seasonings
Divide among bowls and top with the toasted chickpeas and more black pepper to taste.