Gently heat the milk until tepid, then stir in the yeast.
Combine the flour, sugar and 1 teaspoon of sea salt in an electric mixer or another large bowl.
Using your hands or the mixer’s dough hook on medium, work in the butter till the mix is like fine breadcrumbs.
With a wooden spoon, stir in the caraway seeds (if using) and yeasty milk until well combined. It will appear a bit wet, but don’t add any flour. Rest the dough for 10 minutes.
Skip this stage if using an electric mixer. Grab a handful of dough, stretch it out and slap it back into the bowl. Continue to stretch and slap for 5 minutes until it’s more elastic and easier to handle.
Turn the dough out onto a flour-dusted work surface and, with floured hands, knead it for 8 to 10 minutes (or 6 to 8 minutes using the mixer’s dough hook) until it is smooth and elastic.
Place the dough in a large clean bowl, cover with a damp tea towel and leave in a warm place for 1 hour 30 minutes, or until doubled in size.
Preheat the oven to 190ºC/gas 5. Line a baking tray with greaseproof paper (or use a non-stick baking tray).
Knock back the dough and turn it out onto a work surface. Divide into 12 equal pieces and roll into balls.
Place them seam-side up and push a sugar cube into the centres. Pull the dough around it so it is completely enclosed. Reshape into balls.
Place sugar-side down on the tray and cover with a damp cloth. Leave in a warm place for 30 minutes, or until doubled in size.
Beat the egg, then brush over the buns. Bake for 15 to 20 minutes, or until they are golden and sound hollow when tapped underneath.
Just before you take them out the oven, warm the milk and sugar for the glaze until the sugar has dissolved.
Transfer the buns to a wire rack and brush generously with the milk glaze while they’re still hot.
Lightly crush the sugar cubes for the topping, then sprinkle on top with the caraway seeds (if using). Eat while warm.
The buns will last for 3 days in an airtight container, but you may want to reheat them before eating.