01 -
In a small bowl, stir together the warm water and the yeast. Let the mixture stand until it is foamy, about 5 minutes.
02 -
In the bowl of a stand mixer fitted with a dough hook, combine the yeast mixture, warm milk, sugar, melted butter, and 2 of the beaten eggs. Beat on medium-low speed until combined, about 30 seconds.
03 -
Add the flour and salt to the mixer bowl and mix with a spatula until a shaggy dough forms. Return the bowl to the mixer; increase the speed to medium and beat until the dough is smooth, elastic, and tacky, about 5 minutes.
04 -
Transfer the dough to a large bowl lightly greased with nonstick cooking spray. Cover the bowl with plastic wrap and let the dough rise at warm room temperature until it is doubled in size, 1 to 1 1/2 hours.
05 -
Turn the dough out onto a lightly floured surface and divide it into 3 equal portions (about 12 ounces each). Roll each of the portions into an 18- to 20-inch long rope. Braid the ropes together, pinching the ends to seal and tucking them underneath.
06 -
Transfer the braid to a parchment-lined baking sheet. If using, tuck dyed eggs into the braid, spacing them evenly apart. Cover the loaf loosely with plastic wrap and let it rise at warm room temperature until it has puffed, 30 to 45 minutes.
07 -
During the last 30 minutes of proofing, preheat the oven to 350°F. Uncover the loaf and brush it lightly with the remaining beaten egg.
08 -
Bake the loaf until it is golden brown, 28 to 32 minutes. Slide the loaf and the parchment paper onto a wire rack to cool completely, about 1 1/2 hours.
09 -
In a medium bowl, whisk together the powdered sugar and milk until smooth. (Add a touch more milk, if needed to make a smooth, pourable glaze). Drizzle the glaze over the cooled loaf and decorate with sprinkles, if desired.