1. In a small pot, heat the milk until warm but not hot. (approximately 105 Fahrenheit).
2. Pour milk into a medium bowl, and add the sugar, stir to dissolve.
3. After the sugar is dissolved, add the yeast, give one good stir and then let the mixture rest for five to 10 minutes.
4. In a separate bowl, add flour and salt, whisking to combine.
5. While the yeast mixture is resting, melt the margarine and lightly beat the two eggs, then add the eggs and margarine to the yeast and mix until everything is combined.
6. Add the yeast mixture to the flour mixture and mix them together until a tacky dough forms. The dough should pull easily from the sides of the bowl. It should be slightly sticky but should not stick to your fingers when you touch it. (If the dough is too sticky, add more flour one tablespoon at a time until you reach the desired consistency, if it is too dry, add more milk one teaspoon at a time.)
7. Once dough is formed, let it rest for about 10 minutes, then wrap in plastic wrap and refrigerate for two hours to overnight.
8. After the dough is chilled, put onto a lightly floured work surface and roll to about 1⁄2 inch thick. Cut circles out of the dough using a cookie or donut cutter and cover with a towel to let them rest and rise (approximately one hour).
9. After the donuts have risen, heat oil in a fry safe pan with deep sides to 350 degrees. (There should be two to three inches of oil in the pot.)
10. The donuts will rise up almost immediately. After a few minutes, carefully flip using a metal spatula or tongs. Once the donuts are golden brown on both sides, carefully remove from the oil and place on a paper towel lined plate.