Fish: Mince parsley, basil and shallots in a food processor or by hand; place in plastic bag with oils and salmon; seal and turn to coat salmon completely; refrigerate 2 hours or overnight; turn occasionally.
Sauce: Simmer lemon juice, wine and stock until reduced to 2 T, about 12 minutes; add half and half and boil until reduced to 1/4 cup, 2-3 minutes.
Puree the reduction, anchovy and mustard in a blender or mini-processor and pour back into saucepan.
Whisk the butter in, over low heat, 1 T at a time, letting each piece melt before adding the next; set aside and add 1 T capers, salt and cayenne.
Finish: Gently pat marinade off salmon with paper towels; put on aluminum foil if grilling or on broiler pan, skin side down; grill or broil until opaque, 8 minutes depending on fillet thickness.
Plate and spoon 2 T sauce over each fillet and garnish with remaining capers.