Place the bowl of chilled dough in a warm place for 1 hour to make the dough warmer and more pliable.
While the dough is warming, prepare the filling by mixing all the ingredients in a bowl to form a smooth paste. If it is too dry to spread easily, add an extra tablespoon of softened butter.
Punch down the dough and roll it out into a 9x24-inch rectangle. Spread the filling on the dough, leaving a border one inch all the way around.
Roll the dough into a tight log like a roulade, starting from one of the long sides. Pinch the seam and ends to seal.
Use a sharp knife to cut the log in half lengthwise, then turn the two halves so the filling faces upwards. Twist the two lengths together, keeping the filling side up.
Place the bread in a parchment-lined 9x5-inch loaf pan, tucking the ends under, and cover with plastic wrap. Let the loaf rise until it has crowned above the edge of the pan and slowly springs back when prodded with a fingertip, about 1 hour at room temperature.
About 30 minutes before the loaf is done proving, preheat the oven to 350°F.
Bake the babka at 350°F for 50 minutes. It should be well browned and have an internal temperature of 190°F on a meat thermometer when it's done. Check it frequently and cover with foil after the first 20 minutes if it starts getting dark. While the babka is baking, combine the granulated sugar and water in a small saucepan over medium heat until the sugar has dissolved. Set aside.
Brush the babka with all of the sugar syrup. While this step is optional, it does improve the babka’s moisture and helps it stay fresh longer.
Let the babka cool for 15 minutes in the tin. Remove it from the tin and place on a wire rack to cool completely, about 1½-2 hours. Slice and serve.