Roast the peppers and, when they are cool enough to handle, skin and de-seed them. Cut the peppers into strips.
Heat the butter and oil in a skillet, then add the garlic and anchovy fillets. Cook over gentle heat for a couple of minutes, until the anchovies have melted, stirring constantly.
Discard the garlic and add the pepper strips. Let them simmer in the anchovy sauce for a few minutes, just long enough so that the flavors meld.