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Step 1
Proof the yeast. Dissolve the teaspoon of sugar in the warm water, then sprinkle the yeast on top. After a couple of minutes, stir it in.
Step 2
Put the flour in a big bowl along with the salt. Gently heat the milk in a saucepan until it is warm—about 95 – 100º but no warmer. Add the vanilla, the remaining 1/2 cup of white sugar and the olive oil and whisk together. Then whisk in the 3 eggs and the 2 egg yolks.
Step 3
Add all liquids to the flour and mix. The dough will become shaggy. Flour a surface and turn the dough out onto it. Knead it about 5 to 8 minutes, until it is supple and lively and smooth.
Step 4
Clean the large bowl, then dry and oil it. Put the dough into the bowl, turning it so it is coated all over with the oil. Cover it loosely—I used a piece of waxed paper.
Step 5
For the first rising, you can put the bowl in a warmish place until it is doubled in bulk. You can also put it in the refrigerator overnight. It will rise more slowly, and the slow rise will give it a more delicious, subtle flavor.
Step 6
Next, mix together the brown sugar and chopped chocolate in a small bowl. Divide it into 6 portions.
Step 7
Pour the dough onto a lightly floured surface. Cut it in half and put one of the halves back into the bowl for now. Cut the half you are working with into three equal hunks (I used a scale to ensure they were about the same weight). One at a time, roll each hunk into a long skinny log and then, using a rolling pin, flatten the dough into a long rectangle, about 12 to 14 inches by 6 inches.
Step 8
Brush the surface of each rectangle with melted butter. Sprinkle one portion of the chocolate and brown sugar mixture on top of each. Press the chocolate firmly into the dough using the flat of your hand. Then gently fold and roll up each rectangle into a log. Seal the edges.
Step 9
Lay all three logs next to each other, seam sides down, on a lined baking sheet. Pinch the tops of all three together, then braid them. Tuck the ends under and pinch them together too.
Step 10
Repeat this process with the other half of the dough to make the second loaf. Cover braided loaves lightly with waxed paper and let them rise in a warm place, like on top of the stove. When they are doubled in size (about 2 hours), brush them with beaten egg white.
Step 11
Preheat oven to 350ºF. Place loaves on upper and lower racks and bake until golden (about 35 – 40 minutes), rotating loaves and swapping racks halfway through. They will be ready when they look gloriously golden and, when you thump the bottom, they sound hollow.
Step 12
Transfer to cooling racks and let cool completely. Serve. Once the loaves are cooled, they can also be wrapped tightly and frozen.