How to Make It
Preheat the oven to 450°. In a small saucepan, combine the walnuts and the milk and simmer over low heat until the milk has reduced slightly, so it just covers the walnuts, about 20 minutes. Cover and keep warm.
Meanwhile, in a small saucepan, cover the potato with water and bring to a boil. Cook over moderately high heat until just tender, about 6 minutes. Drain well.
In a large skillet, heat 2 tablespoons of the olive oil. Add the shallot and cook over moderate heat until softened, about 3 minutes. Add the green pepper and cook, stirring, for 4 minutes. Add the eggplant and 1 tablespoon of the olive oil. Cover and cook, stirring a few times, until the eggplant is just tender, about 4 minutes.
Add the zucchini and the vegetable stock to the skillet, cover and cook for 3 minutes, stirring once. Gently stir in the potato and basil, season with salt and pepper and stir again. Cover the skillet and remove it from the heat.
In a large ovenproof skillet, heat the remaining 1 tablespoon of olive oil until shimmering. Cut each lamb rack in half and season with salt and pepper. Add the lamb racks to the skillet, meaty side down, and cook them over high heat until richly browned on the bottom, about 4 minutes. Turn and cook on the bony side for 2 minutes. Transfer the skillet to the oven and cook the lamb for about 15 minutes, or until an instant-read thermometer inserted in the center of the meat registers 135° for medium-rare. Transfer the lamb racks to a carving board and let them rest for 10 minutes.
Transfer the walnuts and milk to a blender and puree. Return the walnut sauce to the saucepan and rewarm over moderate heat. Stir in the butter and season with salt and pepper. Reheat the vegetables, if necessary. Carve the lamb into chops and serve with the walnut sauce and vegetables.
The creamy walnut sauce would also be wonderful with veal or chicken.