Warm ½ cup of water and ½ cup of milk in a saucepan over low heat until just melted. Remove from heat and stir in ½ cup of unsalted butter until fully melted. Let cool slightly.

In the bowl of a stand mixer, combine the warm liquid, 2 large eggs, ¼ cup of sugar, 4 cups of flour, 1 teaspoon salt, and 2 teaspoons yeast. Mix on low speed, then knead for 8-10 minutes until slightly sticky and elastic.

Add 1 cup of chocolate chips to the dough. Knead briefly on low speed for 1-2 minutes to distribute evenly.

Transfer dough to a greased bowl, cover, and let rise in a warm place until doubled, about 1 hour.

After rising, turn the dough onto a floured surface, divide into 16-18 pieces, and shape each into a ball. Place on a parchment-lined baking sheet.

Cover shaped rolls with greased plastic wrap and let rise until puffy, about 45 minutes.

Preheat oven to 400°F (200°C) while the rolls rise.

Brush tops with beaten egg. Bake for 15-18 minutes until golden brown and hollow-sounding when tapped.

Transfer to a wire rack to cool slightly before serving warm.