Prepare yeast mixture: Warm the milk and sugar in a small pot over low heat to about 30°C (86°F). Add the yeast and stir until dissolved.
Mix dough: In a stand mixer bowl, combine flour, salt, orange zest, orange juice, 2 beaten eggs, and ground cloves. Mix with dough hook, then add milk yeast mixture.
Add butter and prove: Mix on low speed until smooth, add butter, mix until incorporated. Roll dough into a ball, cover, and leave to prove until doubled in size.
Dye eggs: Prepare dye with water, vinegar, and dye in bowls. Add eggs and leave for 20 minutes. Remove and set aside.
Form bread: Cut proved dough into 3 pieces, roll into ropes, plait, and form a circle on a tray. Add dyed eggs to the center, cover, and prove until doubled.
Bake: Preheat oven to 180°C (356°F). Brush dough with egg wash, add sprinkles, and bake for 25 minutes. Cool for 20 minutes before serving.