In a small saucepan or microwave-safe bowl, warm the milk and 120ml (4.1 fl oz) of water until tepid.
Remove from the heat, stir in the yeast and sugar, and leave covered in a warm place for 10 minutes until frothy.
In a large mixing bowl, rub the sifted flour, salt, and softened butter together with your fingertips until the mixture resembles fine breadcrumbs. Make a well in the centre.
Pour the frothy yeast mixture and the beaten eggs into the well.
Stir to combine, then knead for 10 minutes by hand on a floured surface, or in a stand mixer fitted with a dough hook, until smooth and elastic.
Place the dough in a lightly oiled bowl, cover with cling film, and leave in a warm, draught-free place to prove for 40 minutes.
While the dough proves, prepare the filling.
Combine the mixed peel, flaked almonds, and muscovado sugar in a bowl. Melt the 100g (3.5 oz) of butter and set aside. For the glaze, mix the sugar and vanilla with 2 tbsp (30 ml) of boiling water to form a paste.
Once proved, tip the dough onto a floured worktop and knead lightly for one minute.
Divide the dough in half.
Working with one half at a time, roll it out into a rectangle approximately 45 x 30cm.
Brush the surface of the dough generously with some of the melted butter, then sprinkle over half of the almond and peel mixture, leaving a 1cm border around the edges.
Repeat with the second half of the dough.
Starting from the longest edge, tightly roll each rectangle of dough into a log.
Brush the outside of the logs with more melted butter as you go.
Place them seam-side down.
Trim the ends of each log.
Using a sharp knife or dental floss for a clean cut, divide each log into six equal-sized buns.
Place the buns spiral-side up in a lightly oiled 12-cup muffin tin, gently pressing them down.
Brush each bun with some of the vanilla glaze, reserving the rest.
Cover loosely with cling film and let them prove in a warm place for 30–45 minutes, until they have grown by about one-third.
Preheat your oven to 170°C (340°F) / 150°C Fan / Gas Mark 3½.
Bake the buns for 25–30 minutes, until risen and a deep golden brown.
As soon as they come out of the oven, brush the hot buns with the remaining vanilla glaze.
Let them cool in the tin for 10 minutes before transferring to a wire rack to cool completely.
