Spinach is served two ways in this salad: Sauteed with meaty shiitake mushrooms and raw. Red onions pickled in white balsamic vinegar lend brightness, while toasted sesame seeds make an unexpectedly delicious final flourish.
In a saucepan, bring vinegar, sugar, and 1 teaspoon salt to a simmer. Remove from heat; stir in onion. Let cool completely. If desired, refrigerate in an airtight container up to 1 week. Drain, reserving onion and 1/3 cup liquid.
Place spinach in a large bowl. In a large straight-sided skillet or shallow pot, heat 1/4 cup oil over medium-high. Add mushrooms, season with salt and pepper, and cook, stirring occasionally, until tender and golden brown in places, about 15 minutes. Add about one-quarter of spinach and cook just until collapsed, about 1 minute. Immediately spoon mushroom mixture over spinach in bowl; add reserved pickled onion and pickling liquid, remaining 1/4 cup oil, and sesame seeds. Toss to evenly coat. Season with salt and pepper; serve.