Heat the broiler.
Put 3 tablespoons olive oil in a skillet large enough to hold chickpeas in one layer over medium-high heat. When it's hot, add chickpeas and sprinkle with salt and pepper.
Reduce heat to medium-low and cook, shaking the pan occasionally, until chickpeas begin to brown, about 10 minutes, then add chorizo. Continue cooking for another 5 to 8 minutes or until chickpeas are crisp; use a slotted spoon to remove chickpeas and chorizo from pan and set aside.
Add the remainder of the 1/4 cup of oil (1 tablespoon) to the pan; when it's hot, add spinach and sherry, sprinkle with salt and pepper, and cook spinach over medium-low heat until very soft and the liquid has evaporated. Add chickpeas and chorizo back to the pan and toss quickly to combine; top with bread crumbs, drizzle with a bit more oil and run pan under the broiler to lightly brown the top. Serve hot or at room temperature.