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1
In medium bowl, whisk together milk and yeast. Whisk in egg yolks, eggs, melted butter, and vanilla. In large bowl, stir together flour, sugar, salt, and cardamom. Add liquid ingredients to dry and stir to completely combine. Loosely cover with a towel or plastic wrap and let rest at room temperature until doubled in size and surface is covered with large bubbles, 2 to 3 hours. Refrigerate for at least 3 hours, or preferably overnight.
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2
Adjust oven rack to middle position and preheat oven to 375u00b0F. Spray 10-inch tube pan with non-stick cooking spray. In small bowl, combine chocolate, cocoa, and cinnamon.
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3
On a well-floured surface, roll babka dough into a 12 by 16-inch rectangle. Spread softened butter evenly over dough. Sprinkle chocolate mixture evenly over buttered dough.
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4
Starting with the long end, gently roll up babka into a cylinder shape. Pinch seam to seal. Place cylinder into prepared pan, seam down and slightly overlapping both ends of cylinder. Brush top with egg and let rest at room temperature about 30 minutes.
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5
Bake until babka is golden brown and set, and an instant read thermometer inserted into the center registers, 195u00b0F to 200u00b0F. Cool in pan for 45 minutes. Gently run knife around inside edges to loosen babka and remove babka from pan. Cool completely on wire rack, about 2 hours. Serve.
