01 - Combine warm milk and yeast in a small bowl. Let sit for 5 minutes until foamy.
02 - Whisk together flour, sugar, and salt in a large mixing bowl.
03 - Add melted butter, eggs, vanilla, and yeast mixture to dry ingredients. Mix until a shaggy dough forms.
04 - Knead by hand or with a dough hook for 6-8 minutes until smooth and elastic.
05 - Place dough in a greased bowl, cover, and let rise in a warm place for 1 hour until doubled in size.
06 - Add a few drops of each food coloring to separate bowls of sugar. Rub with fingers until evenly colored.
07 - Roll dough to 1/2-inch thickness on a floured surface. Cut out 3-inch rounds using a donut cutter.
08 - Place donuts on parchment-lined trays, cover lightly, and let rise for 30 minutes.
09 - Heat oil to 350°F. Fry donuts in batches for 1-2 minutes per side until golden brown. Drain on paper towels.
10 - Whisk together powdered sugar, milk, and vanilla until smooth.
11 - Dip warm donuts into icing, allowing excess to drip off. Immediately sprinkle with colored sugars in sections for Mardi Gras effect.
12 - Let donuts set for 10-15 minutes before serving.