Activate the yeast: In the bowl of your mixer add the yeast, 1 tablespoon of sugar and the ¼ cup of water. Mix with the dough hook or paddle attachment. Let it rest for 5 minutes, the mixture should be frothy on top. If not, start over with new yeast.
Add remaining dough ingredients: Add the flour, sugar, salt, milk, eggs to the bowl with yeast and mix with the dough hook attachment for 5 to 8 minutes. The dough is ready when it comes clean from the side of the bowl. If too sticky, add a bit more flour, a tablespoon at a time. The dough should be soft and smooth.
Cover and let rise: Place the dough in a lightly greased bowl, cover with a towel or plastic wrap and let it rise in warm, draft-free environment, until doubled in size, about 1 to 1 ½ hours.
Punch, roll and cut the dough: Punch the dough in the center to release the air. Transfer the dough to a lightly floured surface and roll the dough into a 9x12-inch rectangle. Cut the dough into 12 pieces. Place onto a baking sheet lined with parchment paper.
Cover and let rise a 2nd time: Cover with a clean towel and let rise a 2nd time for another 30 minutes. If the dough pieces are too big, you can cut them in half, so you don't end up with gigantic donuts.
Fry donuts: Pour oil in a large Dutch oven or heavy-duty pot and heat over medium heat to 350°F. Cook 3 to 4 donuts at a time, don't overcrowd the pot, about 1 to 2 minutes per side until puffed up and golden brown.
Transfer to a plate: Transfer fried malasadas to a paper towel lined plate or bowl. Continue with remaining malasadas.
Roll in sugar: Roll malasadas in sugar and serve plain or with your choice of jams, lemon curd, custard, or dulce de leche.