01 - Whisk together flour, granulated sugar, yeast, and salt in a large bowl until thoroughly blended.
02 - Combine lukewarm milk, melted butter, and egg in a separate bowl. Pour wet ingredients into dry ingredients and mix until soft dough forms.
03 - Knead dough on lightly floured surface for 5 minutes until smooth and elastic. Place in greased bowl, cover, and let rise in warm place for 1 hour until doubled in size.
04 - Roll dough to ½-inch thickness. Cut rounds using donut cutter or two round cutters (3-inch for donuts, 1-inch for holes).
05 - Place cut donuts and holes on parchment-lined baking sheet. Cover and let rise 20-30 minutes until slightly puffy.
06 - Heat vegetable oil in heavy-bottomed pot to 350°F. Fry donuts in batches 1-2 minutes per side until golden brown. Remove with slotted spoon and drain on paper towels.
07 - Whisk powdered sugar, milk, and vanilla in bowl until smooth consistency is achieved.
08 - Dip warm donuts in glaze, allowing excess to drip off. Immediately sprinkle with purple, green, and yellow colored sugars in sections to create Mardi Gras effect. Let set on wire rack.