Heat the oil in a medium saucepan over medium-high heat, until the oil reaches 375 degrees F.
In a small bowl, combine the warm water, sugar, and yeast. Whisk and set aside, until the yeast activates and becomes foamy, about 5 minutes.
Meanwhile, in a separate medium bowl, add the potato starch, tapioca starch, millet flour, quinoa flour, brown rice flour, psyllium husk, xanthan gum, and salt. Whisk to combine.
When the yeast mixture is foamy on top, add the olive oil and stir to combine. Then pour the liquid into the flour mixture and stir vigorously with a spoon until the mixture is smooth, there are no lumps, and it forms a loose dough.
Divide the dough into five equal pieces, each about 50 g. Roll each piece of dough into a ball. If the dough sticks to your hands, dust a little brown rice flour onto the pieces of dough before rolling them.
Place a piece of parchment paper on a flat surface. Lightly dust with a little brown rice flour. Press the first piece of dough into a flat 4-inch-diameter circle using your fingertips.
Carefully flip the dough off the parchment onto your hand and gently slide the disc of dough into the hot oil. Be very careful not to burn yourself on the oil.
Fry for 45 seconds to 1 minute on the first side, carefully flip the dough without splashing the oil, and cook on the second side for 45 seconds to 1 minute, until golden brown.
Use tongs or a spider to remove the crust onto a paper towel or paper bag to absorb any excess oil. There should not be much.
Repeat steps 6–9 with the remaining balls of dough.
To serve: press a small indent into the top of each fried dough, then fill with your desired toppings and serve.