Preheat the oven to 400°F and place the prepared broccolini on a baking sheet. Drizzle with 2 tablespoons of the olive oil, ½ teaspoon salt and toss to coat evenly. Spread broccolini evenly across the pan. Roast for 10-15 minutes tossing with tongs once half-way through the cooking. You want the broccolini to be tender but remain crisp, approximately 10-15 minutes total cooking time. Transfer the roasted broccolini to your platter you will be serving in.
In a large frying pan, heat the remaining 2 tablespoons oil over medium heat. Add the onion and cook, stirring occasionally, for about 5 minutes, until starting to soften. Raise the heat to medium-high, add the mushrooms and the remaining 1/2 teaspoon salt, and cook, stirring occasionally, for 7 to 10 minutes, until the mushrooms are golden brown. Note: be sure to really let the mushrooms brown. Whenever cooking mushrooms, you will see a lot of liquid released. Continue cooking until the liquid is gone and the mushrooms have browned, before adding the wine. Add the wine and cook for another 2-3 minutes until the mushrooms have absorbed the wine and stir in the pepper.
Spoon the mushrooms over the broccolini and garnish with Parmesean. Feel free to make it your own with the garnish. I ended up serving this dish with a drizzle of good quality EVOO, aged balsamic, and parmesean. This dish is great served warm or at room temperature.