Prepare Wet Ingredients: Warm the water, milk, and butter until melted, about 2-3 minutes over low heat.

Mix the Dough: Combine the wet ingredients with eggs, sugar, flour, salt, and yeast in a mixer and mix for 3-4 minutes on low, then 5 minutes on medium until sticky.

Knead the Dough: Knead for 8-10 minutes until smooth and elastic, adding flour if too sticky. Shape into a ball.

Incorporate Chocolate Chips: Fold the chocolate chips into the dough, knead briefly.

First Rise: Place dough in an oiled bowl, cover, and let rise for about 1 hour until doubled.

Shape the Rolls: Punch down dough, divide into 18 pieces, and shape into balls. Arrange on a baking sheet.

Second Rise: Brush tops with egg wash, cover loosely, and let rise for 45 minutes.

Preheat Oven: Preheat to 400°F (200°C) about 20 minutes before the second rise ends.

Bake the Brioche: Bake for 15-18 minutes until golden brown and hollow-sounding.

Cool: Allow rolls to cool on the baking sheet for 5 minutes, then transfer to a wire rack.