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