Preheat the grill and grease a 23cm square baking dish.
Brush the eggplant slices with oil and place on a baking tray. Grill until browned on one side, about 5 minutes. Set oven to 180 degrees C.
Melt 2 tablespoons of butter in a large frypan over medium heat. Add onions and garlic; cook and stir until softened. Crumble in the veal and cook until evenly browned. Season with salt and pepper and stir in the tomato paste, parsley and beef stock. Simmer over low heat for 15 minutes. Stir in the breadcrumbs, reserving 1 tablespoon for later, remove from the heat and set aside.
Melt the remaining butter in a small saucepan over medium heat. Stir in the flour until smooth, then gradually stir in the milk so that no lumps form. Simmer, stirring constantly, until thickened. Remove from the heat and whisk in the egg yolk.
Place a layer of eggplant on the bottom of the prepared baking dish. Top with half of the veal mixture and half of the feta cheese. Repeat the layers, then place remaining eggplant in a layer on top. Pour the sauce over all and sprinkle with reserved breadcrumbs.
Bake for 45 minutes, uncovered, in the preheated oven, or until browned and bubbly.