Whisk together flour, sugar and salt in a bowl. Warm milk in the microwave for about 45 seconds or until a thermometer reads 100 to 110 degrees. Add milk to the bowl of a stand mixer fit with a dough hook. Stir in 1 teaspoon of sugar. Sprinkle the yeast over the milk and stir to combine. Let stand for about 5 minutes until the yeast starts to foam.
Add eggs, pumpkin puree, vanilla and then the dry ingredients to the yeast mixture. Mix on low speed until combined and then increase speed to medium and mix for about 5 minutes until the dough is smooth.
Add butter and mix on medium about 4 minutes until butter is incorporated and dough comes together but is sticky. Scrape down the sides of the bowl as needed during mixing. Place the dough into an oiled bowl, cover with plastic wrap and place in the refrigerator for 8 hours or preferably overnight.
Scrape out onto a lightly floured surface. Divide the dough into 2 halves. Starting with one disc, roll the dough out on a floured surface to a 12 x 16 rectangle. Spread with half of the nutella to about ½ inch from the sides.
Starting with the long side, roll the dough into a log. Trim off about an inch from each side. Slice the dough down the middle lengthwise into 2 long halves with the layers exposed. Place the end of one of the halves over the top of the other half, pressing together lightly (see pictures above) and then braid the 2 pieces over one another to the bottom, again pressing together lightly. Repeat the last 2 steps with the other dough disc.
Line a 9 x 5 loaf pan with parchment paper leaving an overhang on the long sides. Carefully place the braided dough into the loaf pan, squeezing the ends slightly to fit if needed. Cover with plastic wrap and let rise in a cool place for an hour. Bake at 350 degrees for about 40 minutes or until golden brown and a tester comes out clean. Immediately after taking out of the oven, brush each loaf with half the sugar syrup, using it all. Cool a few minutes in the loaf pan and then transfer the dough using the parchment paper to a wire rack to cool completely.
Combine the sugar and water in a small saucepan and cook on medium-high until the sugar is dissolved. Set aside to cool.
The babka can keep for about 3 days wrapped tightly in plastic wrap and foil or can be frozen for up to a month.