Coat a large bowl with oil and set aside.

Dissolve the yeast and 1 tablespoon of brown sugar in the warmed milk in a small bowl.

Combine 4 1/2 cups of flour, the remaining sugar, zest, anise, and salt in the bowl of a standing mixer fitted with a paddle attachment and mix on low speed.

Add the 4 undyed eggs, the yeast mixture, and the melted butter and continue to mix on low speed until a firm dough forms, adding more flour if necessary.

Transfer dough to a lightly floured surface and knead by hand until it is soft and elastic -- about 10 minutes.

Form the dough into a ball and transfer it to the prepared bowl, turning to coat all sides with oil.

Cover with a clean, damp kitchen towel and set aside to rise in a warm, draft-free place until it doubles in volume -- about 1 hour.

Preheat oven to 350 degrees F.

Punch down dough, turn out onto a lightly floured board, and divide into three equal parts.

Using the palms of your hands, roll out one piece to create a 2 1/2-foot-long rope.

Repeat with the remaining 2 dough pieces.

Braid the three strands together and seal the ends under each other to create a circle.

Transfer to a baking sheet.

Place the dyed eggs, evenly spaced, in the grooves of the braid, cover with a towel, and let rise until doubled -- about 40 minutes.

Brush the loaf with the beaten egg white.

Bake until loaf is golden and sounds hollow when tapped -- about 30 minutes.

Transfer the finished loaf to a wire rack to cool.

Serve at room temperature.