Preparation

Make the dough

• In a small saucepan over medium heat, bring the milk to a boil. Let cool until just warm (110°F), about 30 minutes. Meanwhile, combine 1 cup of the flour with the yeast in the bowl of a stand mixer. Stir in 1/2 cup very warm water (about 120°F), and form into a ball. Cover the bowl lightly with plastic wrap. Set the bowl in a warm spot until the mixture has visible bubbles on its surface, about 30 minutes.
• Put the bowl in the mixer stand, and fit the mixer with the dough hook. On medium speed, beat in the egg yolks, sugar, butter, and salt, scraping the bowl occasionally. With the mixer running, add the milk and continue to beat until combined (it’s fine if there are a few lumps), about 2 minutes. Gradually add the remaining 2 cups flour. Raise the speed to medium-high, and knead until the dough is smooth, about 5 minutes. The dough will be soft and may not form a ball. Stop the mixer, add the vanilla and almond extracts, and continue to mix until incorporated, 1 minute.
• Lightly coat a bowl with the cooking spray. Transfer the dough to the bowl and cover with plastic. Let rise in a warm place until the dough is doubled in size, 60 to 75 minutes.

Make the filling

• Using a hand mixer, beat the egg whites and salt in a medium bowl on high speed until stiff but not dry, 2 to 3 minutes. Gradually add the sugar and continue to beat until the sugar dissolves and the mixture turns glossy and thickens, about 3 minutes. Add the cocoa and beat on low speed until smooth. Turn off the mixer, and fold in the nuts and chocolate with a silicone spatula until well combined.

Shape and fill the dough

• Butter a 9×5-inch loaf pan.
• Gently scrape the dough onto a lightly floured surface (try not to use more than 1 to 2 Tbs. of extra flour). Divide the dough into thirds. Roll one piece of the dough into a 12-inch-long by 5-inch-wide rectangle (the dough will be 1/4 to 1/2 inch thick).

• With an offset spatula, spread about one-third of the filling over the dough, leaving a 1/2-inch border.

• Roll the dough up lengthwise to make a long cylinder. Pinch the dough’s ends and along the long edge to seal. Repeat with the remaining dough and filling.

• Place the three filled doughs next to each other seam side down, and gently braid them together. Transfer to the prepared loaf pan, tucking the ends under. Loosely cover with plastic wrap, and set in a warm place until the dough rises by 50 to 75 percent, about 50 minutes.

Bake and finish the bread

• Position a rack in the center of the oven, and heat the oven to 350°F. Just before baking, in a small bowl, whisk the egg with 1 Tbs. water, and use a pastry brush to brush the dough with the egg wash. Bake the bread until a wooden skewer inserted in the center comes out with only dry crumbs, and the top is a deep golden amber, 45 to 50 minutes. (If the loaf starts browning too deeply during baking, cover the top of the loaf with foil halfway through.) Transfer the loaf pan to a rack, brush the top of the loaf with the butter, and sprinkle with the sanding sugar. Let cool 15 minutes. Run a knife around the inside of the pan, and gently turn the loaf onto the rack to cool completely, about 1 hour. Store in an airtight container at room temperature for up to 3 days.