Warm (do not boil) 1/4 cup of milk on the stove and whisk in your yeast and sugar. Allow this to rest for at least 5 minutes, until the mixture is foamy.
¼ cup milk (or water), 1 tbsp yeast, 2 tbsp sugar
Combine your salt, flour, egg, olive oil, softened butter, and milk into a mixing bowl. Begin with 1 1/2 cups of milk, you can add more as needed when mixing. Next pour in your yeast mixture to the same mixing bowl.
1½ tsp salt, 5 cups all-purpose flour, ¼ cup olive oil, 3 tbsp butter, 1½ - 2 cups milk
Combine your ingredients with the dough hook attachment on low ("stir" on Kitchen Aid mixer). If the dough is too dry, slowly pour in more milk as the mixer is running until the dough comes together and begins to form a ball. The dough will take anywhere from 5-10 minutes to thoroughly combine and come together.
Cover your bowl - you can use a lid, beeswax wrap, plastic wrap, a damp towel, or even a plate - anything to keep the moisture in. Allow your dough to rest until it has roughly doubled. This may take 1-2 hours depending on the temperature in your kitchen.
Once your dough has doubled in size, remove it from the bow and punch it down. Divide into equal parts, the smaller the better as this will help them to cook all the way through. This recipe will make 16 average sized donuts. Shape your pieces into a classic donut shape and allow to rise a second time. The second rise will take about one hour.
Once your donuts have risen, heat oil on the stove to 350o - 375o F. Fry about 1 minute per side, or until each side is deep gold. Using a slotted spoon, remove the donuts and allow them to dry and cool on a wire rack.
4-8 cups oil
To glaze your donuts, simply whisk your powdered sugar and milk (or water) together to reach a runny consistency. Dip your donuts in the mixture and allow to dry again.
2 cups powdered sugar, 4-5 tbsp milk (or water)