Ideally you should start the day before you want to bake the babka. Place the flour, sugar, yeast and salt in a large bowl or the bowl of a stand mixer fitted with a dough hook. Mix to combine.
Add the pumpkin puree and milk and mix to form a rough dough. Knead until it forms a smooth ball.
Add the softened vegan butter. Continue to knead until the butter is fully incorporated and the dough is smooth and elastic. It may seem greasy and messy at first but keep kneading and I promise you the butter will all mix in and the dough will become smooth.
Once the butter is fully incorporated the dough should look smooth and silky and it should pull away from the sides (but not the bottom) of the bowl cleanly. It should still be soft and sticky but if it seems too wet then you can knead in a little more flour; be careful not to add too much however.
Place the dough in a lightly oiled bowl, cover and leave to rise for 1 hour at room temperature then place it in the fridge to finish rising overnight.
The following day the dough should have doubled in size. Remove it from the fridge and set aside to warm up a little while you prepare the filling.
Chop the pecans very finely. Mix the softened butter, sugar, pumpkin spice, vanilla and a pinch of salt to a smooth paste then stir in the chopped pecans.
Punch down the dough and roll it out on a lightly floured surface to a rectangle about 30x40cm / 11x15in.
Spread the filling evenly over the dough, leaving a 1cm border. Roll the dough up tightly from one of the long edges into a sausage.
Use a sharp knife to cut the sausage in half lengthwise, exposing the filling. Twist the two halves together into a braid.
Grease an approx 11.5 x 21.5 cm / 4.5 x 8.5 in 2lb loaf tin and line it with baking parchment. Place the babka in the loaf tin, squishing it to fit if need be. Loosely cover the tin and set aside to rise until doubled in size, about 1 ½ - 2 hours depending on how cold it is.
It is ready to bake when it looks puffy and if you gently press some of the exposed dough with a finger it springs back slowly most of the way but leaves a small indentation. If it springs back quickly and fills in completely then it isn't ready yet.
When the babka has nearly finished rising, pre-heat the oven to 180°C/160°C fan/350°F/gas mark 4.
Bake the babka for about 45-50 minutes until deep golden. A probe thermometer inserted into the centre should reach about 90°C/195°F when it is ready. If it starts to colour too quickly then loosely cover it with tin foil about half way through baking.
While the babka is baking prepare the syrup. Place the sugar and water in a small pan over a medium heat. Stir until the sugar has dissolved and the syrup comes up to a simmer. Remove from the heat and set aside.
When the babka is ready, remove it from the oven and brush generously all over the top with the syrup. Keep going until you have used all of the syrup.
Leave the babka to cool in the tin for 15-20 minutes while it absorbs the syrup then carefully lift it out onto a wire rack and leave to cool completely before slicing.