How to Make It
Butter a 9-by-13-inch baking dish. In a medium saucepan, melt 1 tablespoon of the butter. Add the shallot and cook over moderate heat until softened. Add the lima beans, stock, bay leaf, 1 cup of water and a large pinch of salt and bring to a boil. Cover and simmer over low heat until the beans are tender, 30 minutes; drain, reserving 1 cup of the cooking liquid. Discard the bay leaf.
Preheat the oven to 375°. In a large, deep skillet, heat the oil. Add the onion and bacon and cook over moderately high heat, stirring occasionally, until the onion is lightly caramelized, 10 minutes. Stir in the garlic, roasted peppers, parsley, thyme and lima beans; remove the skillet from the heat. Stir in the reserved 1 cup of cooking liquid and half of the cheese and season with salt and pepper.
Transfer the lima beans to the prepared baking dish. Sprinkle on the basil, followed by the remaining cheese and the bread crumbs. Dot with the remaining 1 tablespoon of butter and bake in the upper third of the oven for 25 minutes, until golden brown. Let the gratin stand for 10 minutes; serve.