01 - Whisk together flour, granulated sugar, yeast, and salt in a large mixing bowl until thoroughly combined.
02 - Combine lukewarm milk, melted butter, and egg in a separate bowl. Pour wet mixture into dry ingredients and stir until a soft, sticky dough forms.
03 - Turn dough onto lightly floured surface and knead for 5 minutes until smooth and elastic. Transfer to greased bowl, cover, and let rise in warm area for 1 hour until doubled in bulk.
04 - Roll dough to ½-inch thickness. Cut into rounds using 3-inch donut cutter or two round cutters (3-inch outer, 1-inch inner). Arrange on parchment-lined baking sheet, cover, and rise 20-30 minutes until puffy.
05 - Heat oil in heavy-bottomed pot to 350°F. Fry donuts in batches for 1-2 minutes per side until deep golden brown. Remove with slotted spoon and drain on paper towels.
06 - Whisk powdered sugar, milk, and vanilla extract until smooth and pourable consistency is achieved.
07 - Dip warm donuts into glaze, allowing excess to drip off. Immediately sprinkle sections with purple, green, and yellow colored sugars. Transfer to wire rack and let set completely.