• Add the warm milk, yeast, and sugar to the bowl of a stand mixer fitted with a dough hook attachment. If using active dry yeast, let this mixture sit for 5-10 minutes until foamy.
• Add eggs, flour, vanilla, and salt to the milk mixture and mix until it forms a thick dough.
• Next, add in the room temperature butter, a few cubes at a time, and keep mixing to incorporate the butter.
• Turn the mixer to medium speed and keep mixing until the sticky dough strengthens and passes the windowpane test. It should pull away from the sides of the bowl. For the best gluten development and babka crumb, mix for at least 15 minutes. The dough should feel very soft but strong.
• Shape the dough into a ball on a lightly floured work surface, then place it into a lightly oiled bowl. Cover the bowl with a lid or plastic wrap and let it proof in a warm place until doubled in size. 
• Overnight fridge proof - The dough can rise further in the refrigerator for extra flavor before being shaped. This is an optional step. Let the dough rise at room temperature for an hour, then cover it tightly and place it in the refrigerator for 8-16 hours. The chilled dough will be stiff the next day, but it will loosen up when shaping it. 

Shaping

• Beat the softened butter, brown sugar, and cinnamon into a creamy paste in a large mixing bowl. Set aside. Grease and line two 9x5 inch loaf pans with parchment paper.
• Deflate the dough and pull it from the bowl onto a lightly floured surface. Weigh the dough on kitchen scales and cut it into two equal pieces.
• Use a rolling pin to roll one piece into a rectangle measuring around 11x14 inches (27x35 cm).
• Dollop half the cinnamon-sugar mixture over the rectangle in little pieces. Use an offset spatula to spread it out, leaving a ½ inch (1cm) border around all the sides. Roll it up, from the long side upwards, into a log, jelly roll style. Place it in the fridge for 15 minutes. This will make it easier to cut later. Repeat with the other dough piece and the remaining filling. 
• Once chilled, slice a log in half lengthwise with a sharp knife.  Lift the left half over the right half in the middle of the dough, and repeat down and up, to make a braid. When you reach the ends, tuck the dough underneath to compact the loaf. Place the braid into a prepared loaf pan.
• Repeat the process with the second half of the dough. Let the babkas undergo a second rise until they nearly double in size. This can be between 1-2 hours. The rising time depends on room temperature.

Baking

• Preheat the oven to 350°F/180°C and place a rack in the middle.
• Once risen, bake the risen babkas for approximately 35-40 minutes until deep golden brown. If they are browning too much, loosely cover the tops with foil. 
• Combine the sugar and water in a small saucepan over medium heat. Bring it to a simmer until the sugar dissolves, then remove it from the heat. 
• After removing the babkas from the oven, brush them liberally with the syrup. 
• Let them cool In their pans for 20 minutes, then remove and cool them further on a wire rack. Serve the babka at room temperature or slightly warm.