Combine flour, sugar and yeast in a bowl, then add the egg first, then the milk and finally also the softened butter and salt and knead until a homogeneous dough is obtained.
Cover the bowl with cling film or a clean tea towel and let rise for at least 2 hours or until doubled in volume.
Meanwhile, prepare the buttercream: finely chop the garlic, shallot and chives, then mix them together and then add the softened butter, salt, sugar and mayonnaise.
Cut the cheese into thin slices.
Once doubled in volume, take the dough back and place it on the baking sheet lined with parchment paper.
With a fairly sharp, smooth-bladed knife, make cuts with a diamond pattern, then slide the cheese and buttercream into the crevices.
Bake for about 20 minutes or until golden brown in a preheated convection oven at 180 ° C.
The garlic bread is ready, serve it warm or warm to enjoy the melted cheese.
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