Combine 3 cups of flour, 1/4 cup of sugar and salt together in the bowl of your stand mixer. Make a well in the center.
In a small bowl, sprinkle the yeast over the warm milk and add the pinch of sugar. Let sit for 5 minutes.
After the yeast is foamy, pour it into the center of the flour. Add the melted butter and beaten eggs. Attach the dough hook and mix on low speed until a soft dough forms. The dough should be tacky, but not sticky. Add additional flour if it is too sticky.
Turn out the dough onto a lightly floured surface and knead for 1-2 minutes more.
Grease a bowl and place the dough in it, turning it over once to coat. Cover with plastic wrap or a kitchen towel and allow to rise in a warm area until it doubles in size, about 1 hour. (When the bread is rising, prepare the dyed eggs)
Turn the dough out onto a lightly floured surface again. Divide the dough into 12 equal pieces.
Roll each piece out into a 8-10 inch long rope. Pinch the ends of two ropes together and twist over each other like, a braid, then twist the opposite ends together and pinch to seal. This will create a ring-like shape where the egg can sit in the center.
Place on a parchment lined baking sheet and repeat with the remaining dough until you have 6 of them.
Place the dyed eggs inside of each hole and allow to rise again for 1 hour.
Preheat the oven to 350 degrees. Bake for 22-25 minutes or until golden brown.
Remove from the oven and allow to cool on a wire rack.
For the Dyed Eggs:
Follow the directions on the dye package, mixing the tablets into the water and adding vinegar.
Carefully dip the eggs into the dye and let sit for 10-15 minutes each for a dark color.
Transfer the eggs to a drying rack to let dye dry completely.
For the Glaze:
In a medium bowl, whisk together the powdered sugar, milk and vanilla until it reaches drizzling consistency.
Drizzle the glaze over the bread and add sprinkles.
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