1 onion, peeled
1/2 cup sliced pitted Kalamata olives
3 tablespoons plus 1/2 a teaspoon olive oil
1 head garlic
1/2 cup toasted breadcrumbs, or more if needed
1 1/2 cups cooked white beans (cannellini or navy beans)
3 fresh sage leaves, minced
squeeze of fresh lemon juice
freshly ground black pepper
Caramelize the onions: Cut the onion in half through the stem and then slice into 1/8-inch-thick half-rings. Heat 1 tablespoon of the olive oil in a heavy-bottomed sauté pan over medium-low heat and add the onion, turning to coat.
Cook slowly, stirring occasionally and lowering the heat if the onion begins burn, until caramelized, about 30 minutes. Cool.
Meanwhile, roast the garlic: There are many methods, but I prefer this one: Break the head of garlic into cloves and clean off all the papery skins. Toss the cloves in ½ teaspoon of the oil and spread out on a small baking sheet (a toaster oven works.)
Roast at 300°F for 25 to 30 minutes, shaking the pan and stirring the cloves around frequently, until the largest clove can be effortlessly pierced with a knife. Cool.
Preheat the oven to 375°F.
In a food processor, purée ½ cup of the beans with half the roasted garlic, half the caramelized onion, the egg, and half the sage.
Chop the remaining onion and roasted garlic coarsely and place in a mixing bowl. Add the remaining beans and coarsely mash with a potato masher. Fold in the puréed bean-egg mixture, remaining sage, the olives, and lemon juice.
Fold in the bread crumbs, adding more if necessary—just until the mixture begins to pull from the side of the bowl (it will be a wet mixture). Season with salt and pepper. Adjust seasonings. Shape into 4 patties.
In an oven-safe skillet or nonstick sauté pan, heat the remaining 2 tablespoons oil over medium-high heat. When hot, add the patties and cook until browned on each side, 6 to 10 minutes total.
Transfer the pan to the oven and bake for 12 to 15 minutes, until slightly firmed and cooked through.