Step 1: In a large bowl, dissolve the yeast in the warm milk with a tablespoon of the sugar. Let it sit for 5-10 minutes until it becomes foamy.
Step 2: Add the remaining sugar, salt, egg, melted butter, and 2 cups of the flour. Beat until smooth.
Step 3: Gradually add the remaining flour until a soft dough forms. Knead on a lightly floured surface for about 5-7 minutes until smooth and elastic.
Step 4: Place the dough in a greased bowl, cover with a damp cloth, and let rise in a warm place for 1 hour or until doubled in size.
Step 5: Punch down the dough and roll it out on a floured surface to 1/2-inch thickness. Cut with a donut cutter and place on parchment-lined sheets.
Step 6: Cover and let the donuts rise for another 30-45 minutes until puffy.
Step 7: Heat 2 inches of oil in a heavy pot to 350°F. Fry donuts for 1-2 minutes per side until golden brown. Drain on a wire rack or paper towels.
Step 8: Whisk together powdered sugar, maple syrup, vanilla, and a pinch of salt to create the glaze.
Step 9: While the donuts are still warm, dip the tops into the maple glaze and return to the wire rack to set.