01 - Combine warm milk and yeast in a small bowl. Let sit for 5 minutes until foamy and activated.
02 - Whisk together flour, sugar, and salt in a large mixing bowl until well combined.
03 - Add melted butter, eggs, vanilla, and the yeast mixture to the dry ingredients. Mix until a shaggy dough forms.
04 - Knead by hand or with a stand mixer using a dough hook for 6-8 minutes until the dough becomes smooth and elastic.
05 - Place dough in a greased bowl, cover with plastic wrap or a towel, and let rise in a warm place for 1 hour or until doubled in size.
06 - While dough rises, add a few drops of each food coloring to separate bowls of sugar. Rub with fingers until evenly colored and vibrant. Set aside.
07 - Turn risen dough onto a floured surface. Roll out to 1/2-inch thickness. Cut out 3-inch rounds using a donut cutter (or a glass and small cutter for centers).
08 - Place cut donuts on parchment-lined trays, cover lightly, and let rise for 30 minutes until puffy.
09 - Heat vegetable oil in a large, heavy 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.
10 - Whisk together powdered sugar, milk, and vanilla extract until smooth and pourable.
11 - Dip warm donuts into the icing, allowing excess to drip off. Work quickly while donuts are still warm for optimal adherence.
12 - Immediately sprinkle with purple, green, and yellow sugars in sections or stripes to create a traditional Mardi Gras effect. Let set for 10-15 minutes before serving.