01 - Combine lukewarm milk and yeast in a small bowl. Let stand for 5 minutes until mixture becomes foamy, indicating the yeast is active.
02 - Whisk flour, sugar, and salt in a large mixing bowl. Add eggs, softened butter, vanilla extract, and the activated yeast mixture. Mix until a sticky dough forms.
03 - Turn dough onto a lightly floured surface and knead for 8 to 10 minutes until smooth and elastic. The dough should spring back when pressed lightly.
04 - Place dough in a greased bowl, cover with plastic wrap or a clean towel, and let rise in a warm, draft-free area until doubled in size, approximately 1 hour.
05 - Punch down risen dough and roll out to 1/2-inch thickness. Use a donut cutter or two round cutters (3-inch and 1-inch diameter) to cut out donuts and holes.
06 - Arrange cut donuts on parchment-lined baking sheets, leaving space between each. Cover and let rise for 30 minutes until puffy.
07 - Divide sugar into three separate bowls. Add a few drops of purple, green, and yellow food coloring to each bowl. Rub with fingers until evenly colored and vibrant.
08 - Heat vegetable oil in a large pot or deep fryer to 350°F. Fry donuts in batches for 1 to 2 minutes per side until golden brown. Remove with a slotted spoon and drain on paper towels.
09 - Brush warm donuts lightly with melted butter. Immediately dip or sprinkle with colored sugar in alternating purple, green, and gold bands to create the classic Mardi Gras pattern.
10 - Serve donuts fresh and warm for the best texture and flavor experience.