1Crumble tarragon between your fingers into a saucepan over medium heat; add vinegar, bring to a simmer, and cook until vinegar is almost completely evaporated, 1 to 2 minutes. Remove from heat and transfer to a bowl to cool.
2Whisk mayonnaise, dill pickles, bread-and-butter pickles, capers, green onions, parsley, anchovy paste, Dijon mustard, paprika, black pepper, cayenne pepper, salt, and tarragon mixture together in a bowl. Cover with plastic wrap and refrigerate until flavors blend, 8 hours to overnight.