Preheat oven to 350°F. Line a baking sheet with parchment paper and set aside.
In a large mixing bowl, combine the flour, cheeses, 1 ¼ cups yogurt, 1 teaspoon of salt and ½ teaspoon of pepper. Stir with a fork until moistened. You can add about 1-2 tablespoons more yogurt to help the dough come together.
Using a 2-inch ice cream or cookie scoop, drop mounds of dough onto the prepared baking sheet. Sprinkle more cheese on top, if desired, and freshly ground black pepper. Bake for 13-14 minutes or until the cheese has melted and the tops look golden brown.
Meanwhile, in a 10-inch cast iron pan, heat 3 tablespoons olive oil over medium-high heat until shimmering. Add the onions and mushrooms, a generous pinch of salt and pepper and cook, stirring occasionally, until mushrooms are browned, about 10-12 minutes. Reduce the heat to medium. Whisk in 1 ¼ cups water and 1 tablespoon flour and cook until thickened, about 2 minutes. Reduce the heat to low and stir in the remaining yogurt. Cook until heated through. Adjust the seasonings and stir in thyme, if using.
Place biscuits on top of the gravy and serve warm.
Notes
If you can’t find self-rising gluten-free flour, make your own by using 1 teaspoon of baking powder and ½ teaspoon of baking soda per every one cup of flour.