For the anchovy sauce: Rinse the anchovies under cold running water, pat dry and chop. Peel the garlic and chop finely (or press through a garlic press). Heat the butter over medium heat, add the garlic and sauté gently (don't brown). Gradually pour in the olive oil and heat gently over very low heat, stirring frequently and making sure the garlic doesn't burn. Remove the pan from the heat. Mash the anchovies with a fork and carefully add to the sauce. Return to the stove, stir over low heat until creamy.
For the ricotta: Stir together the ricotta or quark with the cream and the lemon zest, season with salt and pepper. Thinly slice the chives and stir into the ricotta mixture.
Serve radicchio or chicory with the dipping sauces. If desired, serve with cut up raw vegetables.