Heat oven to 400 degrees. On a rimmed baking sheet, drizzle peppers with 1 tablespoon oil. Season with salt and pepper and toss to coat. Roast until tender, about 18 minutes. Let cool slightly, then rub off skins and remove stems and seeds.
In a food processor, puree chickpeas and garlic until very smooth, 1 to 2 minutes. Add roasted peppers and vinegar and puree until combined. With machine running, drizzle in remaining 2 tablespoons oil. Season with salt and pepper. Serve with radishes.
Swap out the peppers and combine the base chickpea butter with cooked dark leafy greens, eggplant, broccoli, carrots -- whatever vegetable you have on hand.