Drain anchovies over a large nonreactive skillet to reserve packing oil. Separate anchovies into filets and chop finely.
Peel and seed half the tomatoes and chop them coarsely.
Add butter and a small amount of olive oil to pan with anchovy oil. Add chopped tomatoes, half the chopped anchovies, garlic, onion, and cayenne and cook over low heat, covered, for 45 minutes, stirring f