Preheat oven to 350°. In a pie pan, toss almonds with 1/2 tsp. each water and oil, 1/4 tsp. salt, and the piment d'Espelette. Bake until nuts are golden, 10 minutes. Let cool, then roughly chop. Set aside.
In a small bowl, whisk together verjus, mustard, 1/2 tsp. salt, and 1/4 tsp. pepper. Gradually whisk in 1/4 cup oil. Set aside.
Heat a large cast-iron griddle or skillet over medium-high heat. Brush onion all over with 1 tsp. oil and sprinkle with 1/4 tsp. each salt and pepper. Cook slices flat on griddle until slightly blackened, turning once, 5 to 8 minutes total. Transfer to a bowl, separating into rings. Cover and let sit about 5 minutes to soften.
Meanwhile, cut squash crosswise into 1/2-in. rings and scrape inside clean with a knife. Wipe griddle clean and reduce heat to medium. Toss squash with remaining 1 1/2 tsp. oil, 1/2 tsp. salt, and 1/4 tsp. pepper. Cook squash until browned, turning once, 7 to 8 minutes total. Turn off heat, cover pan, and let squash sit until tender, 20 minutes. Let cool. Shave cheese with a vegetable peeler.
In a large bowl, toss lettuces with half of dressing and salt and pepper to taste. Arrange squash and onion at edges of dinner plates. Drizzle with some dressing. Mound lettuce on plates, sprinkle with nuts and pomegranates, and tuck in cheese. Drizzle with more dressing.
*Find fleur de sel sea salt at gourmet grocery stores. Find ground piment d'Espelette, a fruity, mild chile, at surlatable.com; verjus at sweetwatercellars.com; Mezzo Secco at vellacheese.com; and Little Gem at farmers' markets and well-stocked grocery stores.
Make ahead: The almonds and dressing, up to 1 day (chill dressing and bring to room temperature to serve). The onion and squash, up to 3 hours at room temperature.