Measure the yeast and sugar into a small bowl. Add the water and whisk together till the yeast is soft and it starts to activate. Little bubbles on the surface is a sign of activation. Set aside.
Measure the flour, baking powder, baking soda and salt into a mixing bowl. Make a well in the center. Add in the activated yeast. Use a dough hook with an electric mixer, or a wooden spoon to just start to combine it all together.
Add in the egg and oil. Start to work those into the other ingredients. Measure in all the buttermilk and using the dough hook or a wooden spoon, work it in completely. The dough will be very soft and sticky.
Lightly spray or rub a large clean bowl with olive oil. Turn the dough over into the prepped bowl. Scrape all the sides down. Cover the bowl with a clean dish or tea towel. Set in a warm place for 1-2 hours.
The dough will only slightly rise. Punch it down.
Prepare a large baking sheet with 2-3 layers of paper towels so it is ready to collect the fry bread as it cooks. Heat the 4 cups of oil in a deep skillet. (Use less than 4 cups if the skillet is smaller.) Heat over medium heat. Using flour on a clean, dry surface, work little bits of dough at a time into ping pong ball sized pieces. (about 1 inch) Use flour on your fingers and on the surface to prevent sticking. Roll each piece to about a ¼ inch thick. The circles and ovals should be about 4 inches. They tend to vary in size and shape a little bit.
Fry each rolled out piece one side at a time before flipping over and frying the other side till golden brown. Use a large slotted spoon or web strainer to turn them over and lift them out of the oil and onto the prepared baking sheet. Cook 2-4 at a time in the hot oil. **DO NOT leave hot oil unattended! If you are easily distracted, then finish rolling out all of the dough before starting to cook them. If you are going back and forth between rolling out and cooking, then keep a timer going, or have a second person to help keep their eyes on the oil. Turn the oil heat OFF.
Serve with chili and toppings for Navajo Tacos, or with butter, honey, jams and powdered sugar for dessert.