In a medium saucepan over medium heat, melt the butter and then add the milk and stir. Turn the heat to low and stir in the eggs and egg yolks. Heat the mixture, stirring occasionally, until it reaches 120–130°F (49–54°C). Do not walk away! The eggs will cook if you let the mixture get too warm. Remove from the heat and stir in the vanilla.

Add the liquid mixture to the bowl of the stand mixer and use a rubber spatula to stir it in.

Fit the stand mixer with the dough hook attachment and knead the dough for 10 minutes. The dough will still be quite sticky when finished.

Place the dough in an oiled bowl, cover it with plastic wrap that has been sprayed with cooking spray or lightly oiled. Turn on your oven to the lowest setting for 1 minute and then turn it off. Place the bowl of dough on the center rack, close the oven door, and let the dough rise for 1 hour or until doubled.

Meanwhile, prepare the filling by mixing all the ingredients together in a large bowl. I found this easiest to do with my hands. Set the filling aside.

Mix together all the streusel ingredients in a small bowl and set aside.

Prepare two 9" x 5" loaf pans with parchment paper. Using parchment paper allows for easy removal of the loaves. If you just grease the pans, you'll probably have difficulties removing the loaves if some of the chocolate melts against the pan.

Prepare a Silpat or piece of parchment paper by sprinkling flour over it.

Once the dough has doubled, remove the bowl from the oven. Gently punch the dough down and then pull the edges of the dough to the center, making a ball.

Divide the dough in half (about 21 ounces each half) and place one ball back in the bowl. Cover it up until ready to use.

Place the other ball on the prepared Silpat and knead the dough a few times to help release additional air bubbles. The dough should not be sticky at this point. If it's not very workable, add a little flour and knead it in.

Sprinkle a little flour on top of the dough and lay another Silpat, piece of parchment paper or a piece of plastic wrap on top of the dough. Use a rolling pin to roll it out to a 16" x 10" rectangle (this is approximately the size of a Silpat).

Reserve 1/2 cup of the filling and sprinkle half of the remaining filling evenly over the dough, leaving about a 1" border on all sides.

Starting on one of the short sides, tightly roll up the dough, but only halfway.

Roll the other half of the dough almost until the center (note that in my picture, I should have rolled it a little more!)

Sprinkle 1/4 cup of the reserved filling on top of the side you just rolled up (noting that I added way too much in the picture!)

Carefully place the first side you rolled up on top of the other side and pinch the two sides together to seal it well. It's okay if some chocolate crumbles escape.

Gently twist the roll as if you were wringing out a towel. Cut off 1" of dough on both sides. This is to guarantee that the ends of the loaf are chocolatey and not just doughy. Roll the dough you cut off into a small ball and set aside.

Form a 'u' shape with the dough.

Take the closed end of the 'u' in one hand and the other end in the other hand and twist it as you did before. If it rips a little and a little chocolate falls out, don't worry. The streusel will cover it up!

Place the babka in the prepared loaf pan (noting that it's better to use a piece of parchment paper than oiling the pan, unlike the picture!) and brush the top with the egg white mixture. Evenly distribute half of the streusel on top of the babka.

Repeat with the other half of the dough and let the loaves sit, lightly covered with plastic wrap, for 30 minutes.

Fifteen minutes into the sitting time, preheat the oven to 350°F (175°C).

Place the small balls of dough that you cut off earlier in a small baking dish, a sturdy muffin liner or whatever you'd like to bake them on and bake for only about 17–25 minutes. Bake the babkas for 40–45 minutes or until they sound hollow when tapped and the tops are golden brown. If they brown too quickly in the oven, cover the loaves with foil.

Remove the loaves from the oven and let them cool for 10 minutes in the pan and then remove, with the help of the parchment paper, to a wire rack to cool completely.

Let the loaves cool completely before slicing into. If you cut into them too early, you're likely to end up with dry babka on the next day.

Wrap the loaves in plastic wrap and store in an airtight plastic bag at room temperature. Keeps fresh for 3-4 days.