While the chickpeas are simmering, heat a cast iron skillet over a medium-high heat. Add enough olive oil to cover the base of the skillet and heat through for about a minute.
Add broccolini, a decent pinch of salt, and cover. Cook for 4 minutes. Uncover and stir. Cook for another 1-2 minutes until broccolini is tender, bright green, and charred in spots.