In a medium bowl add yeast, 1 tsp (5g) sugar and ⅓ cup lukewarm milk. Let it rest for 5-10 minutes to activate the yeast.
In a large bowl whisk together the flour, sugar and salt. Add the remaining milk, activated yeast, beaten egg, vanilla extract and melted butter. Start kneading it until it pulls away from the sides of the bowl. You can knead the dough by hand or use a hand mixer or stand mixer.
Divide the dough in two equal pieces. Give the vanilla dough the shape of a ball. Transfer the dough into an oiled bowl and cover with plastic wrap.
Add cocoa powder and milk to the other half of the dough. Continue kneading until the dough is mixed well. Transfer the chocolate dough into an oiled bowl and cover with plastic wrap.
Let the dough rest for about 1 hour at room temperature (warm space) until doubled in size.
Roll the bread.
On an oiled surface roll the vanilla dough into about a 8x12 inch (20x30cm) rectangle.
Repeat with the chocolate dough.
Place chocolate dough over the vanilla dough. Continue rolling to about a 8x 20 inch (20x50cm) rectangle.
Start rolling up the dough almost to the end.
Cut about 10 strips. Twist some of them to alternate colors.
Continue rolling.
Transfer the roll to a 8½ x 4½-inch (1 liter capacity) loaf pan lined with parchment paper.
Let it rest for 30 minutes to room temperature.
How to bake the bread.
Meanwhile, preheat the oven to 350F (180C).
Brush the bread with beaten egg.
Reduce oven temperature to 320F (160C).
Bake for about 40 minutes.
Cover with aluminum foil after about 15 minutes if browns too fast.
Let the chocolate swirl milk bread cool completely before cutting it into slices.