Heat the grill to high. Fry the bacon in the butter until crispy. Drain on kitchen paper and set aside.
Peel and slice the artichokes and put them in a small pan with the cream and milk. Bring to a gentle simmer and cook until tender but still holding their shape, about 10 minutes.
Drain the artichokes and put the liquid back on to the stove to reduce. When thickened to a custar