Bring an 8-qt. pot of well-salted water to a boil. Meanwhile, in a 4- to 6-qt. pot, heat 2 tbsp. oil over medium heat. Add onion and 1 1/2 tsp. salt; cook, stirring occasionally, until translucent, 6 to 8 minutes. "Salt helps pull moisture out of the onion, so it steams and cooks without coloring." Pour in 1/4 cup wine--"to add acidity"--and cook, 1 minute. Stir in spinach, plus pepper to taste, and cook, stirring, until wilted (or just until hot if using thawed frozen spinach). Remove from heat and drain in a colander. "You don't want the liquid--it'll make the lasagna wet."
Preheat oven to 400°. Squeeze sausage from its casing and pull apart into small pieces with a spoon. In a second 4- to 6-qt. pot over medium-high heat, sauté sausage in 1 tbsp. oil until browned, breaking up into nuggets, about 10 minutes. Add garlic and cook until lightly browned, 1 to 2 minutes; then pour in remaining 1/4 cup wine and cook another minute. Stir in tomatoes and simmer 15 to 20 minutes, uncovered--but no more. "You can overcook tomato sauce, and it gets really sweet. For this, you want bright and fresh."
Meanwhile, boil noodles, no more than 6 at a time. "By giving them room, you're making sure they cook evenly and don't stick together." Boil until flexible but still a little underdone (pinch off a piece to test), about 5 minutes. "They'll finish cooking as the lasagna bakes." With tongs, gently lift each noodle as done and dunk for a few seconds in a bowl of ice and cold water to stop cooking, then lift to a large bowl, sprinkle with oil, and turn to coat. "The oil coats the pasta and creates a barrier between noodle and sauce, which helps the texture."
While noodles are cooking, season tomato sauce with salt to taste and about 1 tsp. pepper. "You're basically making a cheater's Bolognese sauce." Toss eggplant slices with a bit of oil and salt, spread out on a parchment-lined baking sheet, and roast in oven 10 minutes. Remove and let cool. (If using summer squash, skip this step.) Blend ricotta with egg in a glass measuring cup. "This stands in for the classic béchamel."
First (bottom) layer: Rub 1 tbsp. oil over bottom of a 9- by 13-in. baking dish. Add cooked noodles (4 crosswise if short and fat; 4 lengthwise if long and thin, and use part of a 5th to fill in the end; overlapping is okay). "Pasta on the bottom, instead of sauce, helps the lasagna cut cleanly." Top noodles with 1/4 of ricotta, smearing into a thin, even layer with the back of a spoon. Top ricotta with 1/3 of spinach. Add about 1/2 cup tomato sauce and spread evenly, followed by 1/2 of basil leaves (tear if large). "Don't put too much tomato sauce. There's nothing worse than a sandwich with messy layers, and I feel the same way about lasagna." Top with 1/3 of mozzarella slices, tearing each slice into large pieces to cover more evenly, then 1/2 of jalapeño slices. "The fresh heat of the chile gives the lasagna a pop."
Second layer: Arrange another level of noodles in pan and gently "smoosh them down. It makes the layers more even." Then layer in these ingredients in order, spreading each evenly: generous 1/4 cup ricotta, 1 cup spinach, 1 1/3 cups tomato sauce--"Double the amount on the first layer, because now you want it to melt down into the other ingredients"--all of eggplant slices (overlap as needed), and all of salami (overlap as needed).
Third layer: Arrange noodles and press down as before. Spread 1 cup tomato sauce, then 1/2 of remaining mozzarella, rest of jalapeño, rest of spinach, and 1/3 of parmesan.
Fourth (final) layer: Top with remaining noodles and press down gently. Spoon on remaining tomato sauce, followed by basil leaves. Evenly dollop on the rest of the ricotta but don't spread. "You want nice little pockets, which will soufflé up and caramelize." Add remaining mozzarella as whole slices, and then rest of parmesan--"a heavy dusting, both for seasoning and for color. I want it to be nice and golden brown."
Bake on center rack 30 minutes, then (keeping lasagna on center rack) turn oven to broil and broil until cheese on top is golden brown and bubbly, 2 to 5 minutes. Remove from the oven and let rest at least 10 minutes before serving.
Make ahead: Through step 8, up to 1 day, chilled, or frozen, up to 3 months. Bring to room temperature before baking.