Make the roux: In a pot, whisk together the flour, water and milk. Continue whisking as it heats up and thickens. Once you have the consistency of a soft paste, remove from heat and allow to cool.
Make the dough: In the bowl of a stand mixer fitted with the dough hook attachment, combine the yeast and milk. Sprinkle a bit of the sugar on top and whisk gently to combine. Give it a few minutes to prove.
Once the yeast mixture is foamy, add the rest of the ingredients as well as the roux. Turn the dough hook on and let it knead the dough until it comes together in a sticky mass, about 5 minutes.
Set the dough in a well-oiled bowl and cover with plastic wrap. Leave in the fridge overnight.
When the dough is nearly done rising, prepare your filling: divide the hazelnut butter or tahini into 5-6 small bowls adding about 3 tablespoons to each bowl.
Melt the white chocolate over a double boiler and then divide it evenly between the bowls. Add food coloring to your liking to each of the bowls.
When dough has doubled in size divide it in two and roll one half out to about 2 inches wider than your loaf pan and about as long as 13 inches.
Spread the filling horizontally on the longer side of the rectangle, in thick ordered stripes.Roll up the babka into a log and slice the babka lengthwise, trim the edges and twist the two halves around each other.
Line a standard loaf pan with parchment paper. Place the babka in the pan and set in a warm place to rise for about 45-60 minutes. Repeat with second dough half.
Preheat oven to 350. Brush the dough sides (avoid the filling) with an egg yolk mixed with a pinch of sugar.
Cover the babka on the top loosely with foil (leaving room at the top for it to rise during the bake) and bake for 25 minutes. Remove the foil and continue baking for another 10 minutes or so, until an instant read thermometer reads 190.
Allow to cool in pan and then remove with the parchment sling. Store in an airtight container.