Preheat oven to 450°F. Toss tomatoes with 3 tablespoons oil, 1/2 teaspoon salt, and 1/4 teaspoon pepper and arrange, cut sides up, in 1 layer in 2 oiled glass or ceramic shallow baking dishes.
Roast tomatoes in upper and lower thirds of oven, switching position of dishes halfway through baking, until skins are wrinkled and beginning to brown, 35 to 40 minutes. Cool slightly in baking dishes on racks.
Roast eggplant for lasagne:
Toss eggplant slices with oil, garlic, 1/2 teaspoon salt, and 1/4 teaspoon pepper and arrange in 1 layer on 2 oiled baking sheets.
Bake in upper and lower thirds of oven, switching position of sheets halfway through baking and turning slices over once, until tender, 12 to 14 minutes. Reduce oven temperature to 350°F.
Finish tomato sauce:
When tomatoes are cool enough to handle, peel off skin and discard. Purée tomatoes with their juices in a blender, pulsing until almost smooth.
Cook onion and garlic in 2 tablespoons oil in a 3- to 4-quart heavy saucepan over moderate heat, stirring, until golden, about 10 minutes.
Stir in tomato purée, water, 1/4 teaspoon salt, and 1/4 teaspoon pepper and simmer, partially covered, stirring occasionally, until slightly thickened and reduced to about 4 cups, about 15 minutes. Stir in basil.
Make filling and assemble lasagne:
While sauce is simmering, cook spinach in a 3- to 4-quart pot of boiling salted water, uncovered, 1 minute, then drain in a colander. When cool enough to handle, squeeze any excess water from spinach and coarsely chop.
Stir together ricotta, yolk, spinach, Parmesan, 3/4 teaspoon salt, and 1/4 teaspoon pepper until combined well. Cook lasagne noodles in a 6- to 8-quart pot of boiling salted water, stirring occasionally, until tender. Drain noodles in a colander and rinse under cold running water.
Spoon 2 cups tomato sauce into a 13- by 9-inch glass baking dish (or other 3-quart shallow baking dish).
Lay out 4 lasagne noodles on a work surface, then spread 1/3 cup filling evenly over each noodle and cover with eggplant slices in 1 layer. Roll up each and arrange spirals, seam sides down and without touching, over sauce in dish, then make 4 more rolls and arrange in dish.
Brush noodles with water, then spoon some sauce down middle of rolls and cover dish tightly with foil. Bake in middle of oven until heated through, about 20 minutes. Heat remaining tomato sauce and serve on the side.