In a large bowl (or the bowl of the electric mixer) mix water, yeast, sugar, salt, eggs, sugar and butter. Add the flour and mix well (do not knead) using your hands, wooden spoon or electric mixer. The dough will be soft but will firm up after proving. Cover and let rise for 2 hours and then chill for at least 2 hours.
Butter a 8x4-inch loaf pan, then line with parchment paper. Use 400-500 g of dough and sprinkle with flour and shape it into a ball, seam side down.
On a lightly floured surface, roll the dough into a 12x16-inch rectangle. Spread the filling on dough, leaving a 1-inch border on one short side. Starting at the short side opposite the border, roll the dough into a log, and pinch the seam to seal.
Cut the dough in half lengthwise and position each half parallel to each other with the cut sides facing up. Twist the 2 long pieces together and place in the prepared pan. Loosely cover the pan and let rise for 1 hour.
Preheat the oven to 350F. Bake the loaf for 35-40 minutes or until golden brown.
For the syrup: while the babka is baking, mix the sugar and water in a small saucepan. Bring to a simmer over medium heat, stirring until the sugar is fully dissolved.
Brush the loaves with the syrup immediately when it come out of the oven. Serve warm or at room temperature.
