On a rimmed baking sheet, toss the mushrooms with 1 tablespoon olive oil, and season with salt and pepper, to taste.
On another rimmed baking sheet, toss the potatoes with the remaining 1 tablespoon olive oil, and season with salt and pepper, to taste. Put both pans in the oven, and roast until the mushrooms are browned and the potatoes are cooked through, about 20 minutes, tossing once and rotating the sheets halfway through. Remove the pans from the oven, and let cool slightly.
While the potatoes and mushrooms roast, make the dressing. Add the garlic, sour cream, yogurt, buttermilk, and vinegar into a food processor and blend to combine. Add the cayenne, herbs, Worcestershire, and hot sauce. Blend until fully incorporated and the dressing is a pale green. Season the dressing with salt and pepper, to taste, if needed.
Add the potatoes and mushrooms to a serving bowl and pour in the dressing. Toss to coat and serve warm or room temperature.