In a large saucepan, heat 2 tablespoons of the olive oil. Add the onion and garlic, cover and cook over low heat until they are softened, about 5 minutes. Uncover and cook, stirring occasionally, until the onion is lightly browned, about 5 minutes longer. Transfer the onion and garlic to a blender or food processor and puree until smooth, about 1 minute.

In a very large, deep skillet, heat the remaining 1 tablespoon of olive oil. Season the chicken legs with salt and black pepper, add to the skillet and cook over moderate heat, turning occasionally, until they are golden all over, about 12 minutes. Transfer the chicken legs to a plate.

Add the onion puree, diced chorizo, piquillo peppers, and butter beans to the skillet and cook, stirring, until sizzling, about 2 minutes. Add the chicken stock and crumbled saffron, season with salt and bring to a boil. Stir in the rice. Nestle the chicken legs into the rice, cover and cook over moderately low heat until the rice is nearly tender, about 18 minutes. Add the peas, mussels, clams, and shrimp, cover and cook until the shellfish is open and the chicken is cooked through, about 8 minutes. Let the paella rest for 5 minutes before serving.

The onion puree can be refrigerated for up to 1 day. Bring to room temperature before using.