Heat 1 ½ cups of milk in a medium saucepan over medium heat until it just begins to simmer. Remove from heat and stir in ½ cup granulated sugar, salt, and butter until melted. Set aside to cool slightly.

In a small bowl, mix warm water with 1 tablespoon of granulated sugar and the yeast packets. Stir and let sit for about 5 minutes until the yeast becomes foamy.

In a stand mixer bowl, combine the yeast mixture and the cooled milk mixture. Add the eggs and mix until smooth using an electric mixer or the paddle attachment of a stand mixer.

Gradually add 1 cup of flour at a time, mixing with the dough hook or by hand as the dough becomes thicker. Continue until all the flour is incorporated.

Transfer the dough to a floured surface and knead for about 5 minutes until smooth and elastic, adding small amounts of flour as needed to prevent sticking.

Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for 60-90 minutes, or until doubled in size.

Punch down the dough, cover it again, and let it rise a second time for 60 minutes.

In a medium bowl, prepare the glaze by mixing powdered sugar, corn syrup, vanilla extract, and ½ cup of milk until smooth. Set aside.

Roll out the risen dough on a clean, floured surface to about 1-inch thickness. Cut out donut shapes using a donut cutter or two differently sized round cutters for the centers.

Arrange the cut donuts on cookie sheets and let them rest while preparing the frying oil.

Fill a large pot, Dutch oven, or deep fryer with at least 2 inches of vegetable oil. Heat the oil to 350°F, using a thermometer to maintain the correct temperature.

Carefully lower one or two donuts into the hot oil at a time, frying for about 1 minute per side until golden brown. Remove and place on a cooling rack over a baking sheet.

Dip warm donuts into the prepared glaze, ensuring even coverage, and return them to the cooling rack to set.

Serve warm for the best flavor and texture.