Heat the milk to 110ºF (43ºC), then stir in the yeast and a pinch of sugar. Let stand for 10 minutes to bubble and proof.
Meanwhile, in the bowl of an electric mixer fitted with the paddle attachment, combine the flours, cardamom, salt, and granulated sugar. Mix well.
After the yeast has proofed and is foamy, whisk in the egg, then pour this mixture into the mixer bowl. Drop in the butter too. Mix with the paddle on medium–low until the dough comes together and all the ingredients are well mixed and hydrated.
Switch to the dough hook. Knead for 6 to 8 minutes until the dough forms a ball.
Transfer the dough to a greased bowl, cover with plastic wrap and let rise in the microwave (turned off, door closed) for about an hour until doubled in size.
Make the filling
Cream together the butter with the muscavado, cardamom, and espresso powder. Set aside.
Assemble and bake the buns
Transfer the risen dough to a lightly floured surface (don't use too much flour!). Roll it out to a 12x16 inch rectangle.
Spread the filling mixture evenly over the entire surface of the rectangle. Fold in half, lengthwise, then cut into 12 strips.
Working with 1 strip at a time, twist and twirl the strip on itself into a spiral, then wrap it around your hand and pull the end through to knot it (see video).
Transfer shaped buns to two large parchment-lined baking sheets. Cover with towels and let rest for 30 minutes to 1 hour.
Preheat the oven to 350 °F (175 °C).
Make the glaze and bake the buns
Just before baking, brush the buns with a little whole milk to moisten them. Bake for about 25 to 30 minutes, until they are a deep golden brown.
While the buns are baking, make the syrup by combining the water, sugar, cardamom, and freshly ground coffee. Bring to a boil and simmer for 3 minutes. Remove the saucepan from the heat and let the mixture steep for 10 minutes, then strain into a heatproof bowl or glass. Mix in the vanilla bean paste.
As soon as the buns are baked, remove the pans from the oven. Immediately brush the buns with the syrup. Give every bun a coat of glaze, then coat them again.
Let the buns cool, then serve immediately
Notes
Vanilla bean paste is an item that you can find in some specialty stores. I like the vanilla bean paste from Nielson Massey, available on Amazon