Melt the oil and butter together in a large pan, and fry the garlic gently until light brown. Add the anchovies and rosemary and then mash them into the oil, almost to a paste. The anchovies do not need to cook, they just melt; this only takes a few seconds.
Add the tomatoes to the paste and stir to break them up. Bring to the boil, then reduce the heat and simmer until the liquid has e