Heat 1 teaspoons olive oil in a large nonstick skillet set over medium heat. Add the shallots and cook until tender, 3 to 4 minutes. Stir in the garlic and rosemary, and cook for 1 minute.
To the skillet, add another 2 teaspoons olive oil, then stir in the crimini, shiitake and Portobello mushrooms.
Cook until the mushrooms start to sweat, sprinkle with ½ tsp salt and stir in red wine.
Increase the heat to medium-high and cook, stirring occasionally, until most of the liquid is absorbed.
While the mushrooms are cooking, heat 2 teaspoons olive oil in a medium nonstick skillet. Add the cauliflower rice and cook until just starting to soften, 3 to 4 minutes. Remove from the heat, season with ⅛ teaspoon salt and stir in Parmesan cheese. Transfer the cauliflower to a bowl and keep warm.
In the same medium skillet, heat 1 teaspoon olive oil. Add the chopped red chard and vegetable broth, and cook until the chard is wilted, 1 to 2 minutes. Season with ⅛ teaspoon salt.
Divide the cauliflower rice between two dinner plates. Top with the chard and the mushrooms. To achieve the domed mushroom look as seen in the photos above, lightly pack them mushrooms into a 1 cup measure, then invert on top of the chard. Slowly lift the measuring cup.
Garnish each portion with parsley. Serve.