Combine warm milk and a pinch of sugar, sprinkle yeast over top, and let stand until foamy. Whisk flour, remaining sugar, and salt. Add melted butter, 3 eggs, zest, anise extract, and yeast mixture. Knead until smooth and elastic, about 8 minutes.

Shape dough into a ball, place in a greased bowl, cover, and let rise until doubled, 1 to 1.5 hours.

Punch down dough. Divide into 2 portions, then each into 3 ropes. Braid ropes, place on baking sheet. Gently press a dyed egg into each braid. Cover and let rise until puffy, 30 to 40 minutes.

Preheat oven to 350°F (175°C). Brush loaves with egg wash if desired. Bake until deep golden and a thermometer reads 190°F (88°C), 25 to 30 minutes, rotating halfway.

Cool on a wire rack at least 15 minutes, then slice and serve warm or at room temperature.