Combine vinegar, honey, 2 chopped cloves garlic, and 1 Tbsp olive oil in a bowl. Season with salt and pepper. Arrange mushrooms in a baking dish. Drizzle with vinaigrette, cover, and marinate, turning occasionally, at room temperature for at least 30 minutes (or overnight in the refrigerator).
Meanwhile, heat 1 Tbsp oil in a large skillet over medium heat. Add onion, 2 thinly sliced cloves garlic, and a pinch red pepper flakes and cook, stirring, until softened, about 5 minutes. Add kale, season with salt, and cook, covered, until bright green and soft, about 4 minutes.
Heat oven to 400 degrees. Roast mushrooms, flipping once, until tender, about 30 minutes. Serve topped with kale.
Refrigerate cooked mushrooms in an airtight container up to two days.