In a stand mixer bowl, add all ingredients (except frying oil): 300 grams Bob's Red Mill Gluten Free Homemade Wonderful Bread Mix, 1 package instant yeast, 50 grams granulated sugar, 1 whole egg, 6 tablespoons unsalted butter, 160 grams milk, 1 teaspoon baking powder and mix on medium speed until a soft, sticky ball forms.
Transfer dough to lightly greased bowl, cover bowl, and rest in the refrigerator for 30 minutes to one hour. This reduces stickiness and makes the dough easier to work with.
Place dough on a lightly floured surface. Sprinkle the dough lightly with flour. Knead the dough a few times until smooth.
Using cutters: Roll the dough out to 1/2-inch thickness. Cut the donuts using a 3–3.5-inch donut/biscuit cutter or large circle cookie cutter. If using cookie cutter, use a much smaller cutter to cut out the center hole.
Hand shaping: Divide the dough into 8 equal pieces. Roll into 8 dough balls and press them flat. Gently pinch the middle to form a hole and smooth out the inner edges.
Place shaped donuts on a pan lined with parchment paper. Lightly brush tops of donuts with oil to keep from drying out. Cover the baking sheets with oiled plastic wrap, and proof the donuts in a warm, draft-free spot for 1-1 1/2 hours. Allow the donuts to rise to about 150% of their original size.
Using a pot and a heating thermometer, heat at least 2 inches of oil to 350-375℉. You will need to make sure the oil maintains this temperature and adjust your stove setting as needed. Test the oil using an extra piece of dough or old piece of bread to begin. If it quickly sizzles up to the surface you know your oil is hot enough. If it sizzles up and browns instantly, the oil is too hot - reduce the heat or turn it off for 2-3 minutes to let the oil cool down slightly and check again.
Fry the donuts, 1-3 at a time, until golden brown or about 1 minute per side. Use tongs or a slotted spoon to turn donuts and to pull out of the oil. Lay fried donuts on a wire rack lined with paper towels.