Melt the butter in a small pot over low heat. Turn off the heat, add the milk and stir to combine. Check it isn’t too hot (you want it luke warm, like body temperature), then sprinkle the active dried yeast over the top. (If this is too hot is can kill the yeast). Leave for a few minutes.
Add the flour and the milk/yeast mixture to the mixing bowl and use the dough hook to knead for 5-7 minutes, until the dough is elastic, smooth and pulls away from the side of the bowl. You can also do this by hand - start off with a spoon because it is a very sticky dough, and it will probably to take closer to 10 minutes.
Leave to cool to room temperature.
Grease and line a 9x4inch (approx 23 x 10 cm) loaf pan.
Use a pastry brush to liberally brush the syrup over the babka. It may seem like a lot, but trust me, it works!