Line an 11x17-inch sheet pan with parchment paper.
Turn out the vánočka dough onto a very large, lightly floured wooden cutting board. Divide it into two pieces, one about 60% of the dough, and the other 40%. Cut the larger piece into five equal pieces, and the smaller piece into four equal pieces. (A bench scraper is helpful for this.)
Gently roll each piece into a rope, then divide the ropes into 3 groups. Put the 2 longest strands in one group, and the 3 shortest ones in another. The remaining 4 strands are the third group.
Place the group of 4 strands side by side and join them together at the top. Stick them to the work surface by pressing down firmly with your thumb. Think of the strands of being numbered from 1 through 4, from left to right. Bring 4 over 3, then bring 2 over 1. Cross the new strand 2 over strand 3. Repeat this sequence until the whole loaf is braided.
Place the braid on the cookie sheet and use the side of your hand to create a valley lengthwise down the center of the braid. Brush the valley with beaten egg.
Lay the group of 3 strands side by side and braid. Pinch the ends to seal, then make a valley down the middle as before. Place the new braid on top of the previous one, making sure it's centered. Brush the valley with beaten egg.
Roll the two remaining strands so they're just a couple inches longer than the loaf, then twist them together tightly. Place the twist on top of the loaf, tucking the ends of the twist under the other two braids.
Cover the sheet pan with a tea towel or plastic wrap and set aside to prove for 1 hour in a warm place. It's ready to bake when the dough slowly springs back when gently prodded with a fingertip.