Prepare the Wet Ingredients. In a microwave-safe bowl or measuring cup, combine the water, milk, and butter. Microwave on low power for 45-60 seconds, just until the butter begins to melt and the mixture is warm. Stir to fully dissolve the butter.
Mix the Dough. Put the warm milk mixture, eggs, sugar, flour (starting with 3 ¾ cups), salt, and instant yeast in the bowl of your stand mixer. Then attach the dough hook to the mixer and start it on a low setting to mix all the ingredients together. After that, increase the speed to medium and knead the dough for about 8-10 minutes. The dough should be slightly sticky but still form a ball that pulls away from the sides of the bowl. If the dough is too sticky (more like a batter), add flour one tablespoon at a time, allowing it to fully mix in before adding more.
Add Chocolate Chips. Once the dough is smooth and elastic, reduce the mixer speed to low and add the chocolate chips. Knead just until the chips are evenly distributed throughout the dough, about 1-2 minutes. Avoid over-kneading as it can break the chips and affect the dough structure.
First Rise. Transfer the dough to a lightly oiled bowl, turning it once to coat all sides with oil. Cover the bowl with plastic wrap or a damp tea towel.Let the dough rise in a warm, draft-free area for about 1 hour or until it has doubled in size.
Shape the Rolls. Once risen, turn the dough out onto a lightly floured surface. Divide the dough into 18 equal pieces. Shape each piece into a smooth ball by pulling the dough from the sides and tucking the ends underneath. If the dough is sticky, lightly oil your hands or use a bit of flour to prevent sticking.
Second Rise. Line a baking sheet with parchment paper and place the dough balls on it, spacing them about 2 inches apart. Gently brush each roll with beaten egg and sprinkle with sparkling or pearl sugar. Cover the rolls loosely with greased plastic wrap. Let them rise again in a warm, draft-free area for about 45 minutes or until puffy and nearly doubled.
Preheat the Oven. During the last 10 minutes of the second rise, preheat your oven to 400°F (200°C) with the rack positioned in the center.
Bake the Brioche. Once the rolls have risen, place the baking sheet in the preheated oven. Bake for 15-17 minutes, or until the rolls are golden brown and sound hollow when tapped. If they brown too quickly, tent loosely with aluminum foil.
Cooling. Remove the rolls from the oven and transfer them to a wire rack to cool slightly. They are best served warm but can be cooled completely and stored in an airtight container.