In blender, add 1/4 cup olive oil, egg, milk, tapioca flour, Parmesan, salt, cayenne, and black pepper. Blend on high, scraping down sides as necessary, until all flour is incorporated. Add thyme and pulse gently to incorporate. Pour this runny batter into prepared muffin cups, filling each halfway. Bake in preheated oven for 20 minutes. Remove from oven and flip each bun using palette knife prised against the side of each cup. Pierce bottom of bun (see tip) and allow to cool in pan for 2 minutes.