In a large mixing bowl, add in the all purpose flour, granulated sweetener, salt and the instant yeast. Whisk together till well combined.
In another small mixing bowl, crack the eggs and separate the egg yolks from the egg whites. Add the cooking oil and the vanilla extract to the egg yolks and whisk till well combined. Next add in the warm milk and combine.
Make a well at the center of the bowl containing the dry ingredients and pour in the wet ingredients. Knead till the dough comes together for about 7-8 minutes. (You can use a stand mixer for this if you have one). You should end up with a soft and slightly sticky dough.
Place the dough inside your mixing bowl and cover with a plastic wrap then allow to rise until it doubles in size, for about 45 minutes in a warm place or 1½ to 2 hours at room temperature.
After the dough has risen, punch it down to remove the air then using a rolling pin, roll to about ½ cm thick. Use a doughnut cutter to cut the dough or a 9 cm round cookie cutter and a 2 cm round cookie cutter for the holes. You should get 12-14 doughnuts and doughnut holes.
Place doughnuts and doughnut holes on baking sheet or tray. Make sure they are not too close to each other as they could touch after rising. Cover them with a plastic wrap or a kitchen towel. Let them rise for about 30 minutes in a warm place or for 45 minutes at room temperature till puffy.
In a cooking pot/ sufuria, add in enough oil for deep frying the doughnuts. Heat till when you insert a wooden spoon, bubbles form around it.
Deep your doughnuts to fry one at a time and avoid crowding the pot. Remember to lower the heat as they cook till golden brown on both sides.
Once cooked, remove with a slotted spoon and place them on a bowl or tray lined with some paper towel or a wire rack to drain the excess oil. If glazing, dip them into the glaze one by one and use a skewer to turn them around so that they are fully coated with the glaze then place on a wire rack to allow the glaze to set.
Repeat the whole process of frying and glazing till done. Serve once done and the glaze has set. Perfect while still warm or cold with a cup of tea, coffee or hot chocolate