In a small bowl, combine warm water, warm milk, and active dry yeast. Stir gently and let it sit for 5-10 minutes until the mixture is foamy.
In a large mixing bowl, whisk together 3 cups of all-purpose flour, cocoa powder, sugar, and salt.
Add the melted butter and egg to the yeast mixture and whisk until combined.
Pour the wet ingredients into the dry ingredients and mix with a wooden spoon or dough hook attachment until a sticky dough forms.
Gradually add the remaining 1/2 cup of flour, a little at a time, kneading until the dough is smooth and elastic but still slightly sticky, about 8-10 minutes by hand or 5-7 minutes with a stand mixer.
Fold in the chocolate chips evenly throughout the dough.
Place the dough in a lightly greased bowl, cover with a clean kitchen towel or plastic wrap, and let it rise in a warm place for 1 hour or until doubled in size.
Punch down the dough to release air and transfer it to a lightly floured surface. Shape the dough into a loaf and place it into a greased 9×5 inch loaf pan.
Cover the loaf pan with a towel and let the dough rise again for 30-40 minutes until it rises about 1 inch above the rim of the pan.
Preheat the oven to 350°F (175°C).
Bake the bread loaf for 30-35 minutes until the top is firm and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Remove the bread from the oven and let it cool in the pan for 10 minutes, then transfer to a wire rack to cool completely before slicing.