In a medium-sized bowl, mix the dry ingredients: flour, yeast, and sugar. Use a spatula to combine them, then add the eggs.
Continue mixing the dough, then add the milk and butter.
Try to form a smooth, rounded dough. Cover the bowl with a kitchen towel and place it in a warm spot to rise for about 2 hours.
Roll each portion of dough into a ball, then flatten it into small discs. Place them onto parchment paper, ensuring the surface is lightly floured. Use a round cutter to cut out the shapes, and for smaller holes, use a 3/4-inch cutter.
Preheat a dish filled with vegetable oil or a deep fat fryer. Carefully place each donut into the oil, cooking 1-2 at a time for about 2 minutes, then flip them to cook the other side. Once cooked, place the donuts on a plate and let them cool.