Cut the tops from the garlic bulbs, exposing the cloves. Place on a 20cm square of tin foil, drizzle with 1 tablespoon of oil, then wrap the foil around them.
Place on a baking tray and cook for 45 minutes, or until very soft. Leave to cool slightly, then squeeze the garlic out of its skins.
While you wait, grease and line a 1.2 litre loaf tin with parchment.
Finely grate the Parmesan, drain and tear up the mozzarella, crumble the Stilton, and pick and tear the basil leaves.
Mix the soft butter with all but 1 tablespoon of each cheese. Add in the basil, plus a pinch of sea salt and black pepper. Set aside.
Add the flour, yeast, baking powder, sugar and salt to a large bowl. In another bowl, beat the whole egg and egg white with the vinegar.
Pour the eggs and 325ml warm water over the flour mixture, stirring with
a wooden spoon until it forms a soft dough.
Shape into a smooth ball, adding a little flour if needed, then set aside for 20 minutes to firm up.
Divide the dough into four pieces, then roll or press each one into a rectangle about 20 x 10cm – you will need to use plenty of flour to stop the dough from sticking to both you and the worktop.
Dot a third of the cheesy butter and a few garlic cloves over the first layer, repeat with other pieces of dough, very carefully layering them on top of each other. Finish with the last layer of dough.
Cut the layered dough widthways into four, then turn each piece cut-side-up and place side by side in your tin. Cover loosely with oiled cling film and leave in a warm place until well risen, about 1 hour. The bread will rise further in the oven, so make sure the bread has filled the tin and feels pillowy before baking.
Preheat the oven to 220C/gas 7.
Scatter with the rest of the cheese, drizzle with a little oil, then bake for 45 minutes or until deep golden brown and sizzling. Eat warm, rather than hot, and on the day it’s made.