Warm the milk and water until lukewarm (about 110°F). Sprinkle the yeast and a pinch of sugar over the warm water and let it bloom for 5 minutes, until foamy.

In a large bowl, whisk together the flour, sugar, and salt. Make a well and add the eggs, vanilla, and yeast mixture. Stir until a shaggy dough forms.

Add the softened butter in pieces and knead (by hand or with a stand mixer) for about 8 minutes until the dough is smooth, elastic, and slightly sticky.

Place the dough in an oiled bowl, cover with a clean towel, and let it rise in a warm spot until doubled, about 1 to 1 1/2 hours.

Meanwhile, make the filling: beat the cream cheese, powdered sugar, vanilla, and cinnamon until smooth and spreadable.

Punch down the risen dough on a floured surface. Divide into two equal pieces and roll each into a long rope about 18 inches long.

Spread the cream cheese filling down the center of one rope, leaving 1 inch at the ends. Place the second rope on top and pinch the edges to seal. Braid the ropes gently, then curve into a circle, pinching the ends together and tucking slightly to form a ring.

Transfer the ring to a parchment-lined baking sheet. Cover and let rise for 30 to 45 minutes until puffy.

Preheat the oven to 350°F. Brush the top lightly with beaten egg for shine. Bake 20 to 25 minutes until golden brown and the bottom sounds hollow when tapped.

While the cake cools slightly, whisk together the powdered sugar, lemon juice, and milk to make a glaze.

Drizzle over the warm ring and sprinkle the purple, green, and gold sugars in bands.

If you are using a baby, hide it under the cake or insert it after baking into the bottom.