In a small food processor or blender, combine the anchovies and oil from the tin, capers, garlic, and lemon zest and juice. Pulse until coarsely chopped.
Meanwhile, melt the butter in a small saucepan or in the microwave.
Add the olive oil to the processor and puree until emulsified. Stream in the hot melted butter and pulse a few more times until combined. Taste for seasoning - the anchovies and capers can be salty, so you don’t want to add more until the end.
To serve, toss vinaigrette with raw kale, escarole, or spinach. Or serve alongside raw vegetables as a more traditional dipping sauce. Dressing can keep for up to a week in the fridge. Reheat slightly in the microwave before using.