Preheat the oven to 200°C/180°C fan/gas mark 6. Wrap the beetroot in foil and place in the oven on a small roasting tray. Bake for 1 hour-1 hour 15 minutes, until soft. Once cooked, leave to cool, then peel off the skin and quarter. Place in a small food processor and blitz until smooth.
Place the milk in a small saucepan and heat until it feels warm but not hot.
Put the flour in the bowl of a free-standing mixer fitted with a dough hook. Place the salt and sugar on one side of the bowl and the yeast on the other side. Add the warm milk, blitzed beetroot and 4 eggs and mix on a slow speed for 2 minutes, then on a medium speed for 8 minutes. Gradually add the cubed butter and mix for a further 5 minutes, making sure to scrape down the bowl to ensure the butter is thoroughly mixed in. The dough will feel soft but not too sticky.
Tip the dough into a large lightly greased bowl and cover with clingfilm. Leave to rise for 1-2 hours somewhere warm but not too hot as the butter in the dough will begin to melt and make it too soft. If it starts to get too soft, you can place it in the fridge to firm up.
Once doubled in size, turn on to a lightly floured surface and lightly knead to knock out the air. Divide into 8 equal pieces (each ball should weigh roughly 140g) then lay out on a large baking tray lined with greaseproof paper, making sure they are spaced well apart. Loosely cover with clingfilm and leave to prove for roughly 30 minutes, until slightly puffed up. Beat the remaining egg and brush over the top, then sprinkle over the black sesame seeds. Bake for 25 minutes, until they are deep golden on the outside and they feel light for their size when lifted up. Leave to cool on a wire rack before filling with your favourite ingredients.