Clean and wash the gizzards. Put them in a pressure cooker, pour in enough water to cover them and boil 40 min. Remove any foam from the broth, add salt, the allspice and bay leaf and boil until ready.
Drain the gizzards from the broth, cut them in 2 and transfer to a pan with the melted and heated together butter and olive oil. Braise until golden.
Add the mixture to the gizzards in the pan, pour in a few tbsp of the broth from the gizzards, stir well for 1-2 min. and remove from the stove.
Distribute the dish into 4 serving plates, decorate each with a sprig of parsley and lemon slice. Serve hot.