Preheat oven to 400°. Put broccolini on a baking sheet, drizzle with 2 tablespoons oil, sprinkle with 1/2 teaspoon salt, toss to coat evenly, and then spread in a single layer. Roast, turning once with tongs, for 10–15 minutes, until crisp-tender. If the broccolini stems are not uniform in size, remove thinner ones as they are done. Transfer to a platter. (The broccolini can be cooked several hours ahead of time and kept at room temperature.)

In a large (12 inches or wider), deep frying pan, heat remaining 2 tablespoons oil over medium heat. Add onion and cook, stirring occasionally, for about 5 minutes, until starting to soften. Raise heat to medium-high, add mushrooms and remaining 1/2 teaspoon salt, and cook, stirring occasionally, for 7–10 minutes, until mushrooms are golden brown. (The mushrooms will release a lot of liquid before reabsorbing it and browning. Be patient, as the flavor is in the browning.) Add wine and cook for about 2 minutes more, until pan is dry. Stir in pepper.

Spoon mushrooms over broccolini, and then scatter some Parmesan over the top. Serve warm or at room temperature.