Preheat oven to 400°F. On a baking sheet, drizzle broccolini with 2 Tbsp. oil; sprinkle with 1/2 tsp. salt and toss to coat. Spread in a single layer. Roast, turning once with tongs, until crisp-tender, 10 to 15 minutes. If stems are not uniform in size, remove thinner ones to a platter as they are done. (Broccolini can be cooked several hours in advance and kept at room temperature.)
In a large, deep frying pan, heat remaining 2 Tbsp. oil over medium heat. Add onion and cook, stirring occasionally, until starting to soften, about 5 minutes. Raise heat to medium-high, add mushrooms and remaining 1/2 tsp. salt and cook, stirring occasionally, until mushrooms are golden brown, 7 to 10 minutes. (Mushrooms will release liquid before reabsorbing it and browning.) Add wine; cook until pan is dry, about 2 minutes. Stir in pepper.
Spoon mushrooms over broccolini. Scatter some Parmesan over dish, if desired. Serve warm or at room temperature.
Adapted with permission from Brassicas, by Laura B. Russell (Ten Speed Press, copyright 2014).