Heat 1 inch of vegetable oil in a medium saucepan until a deep-fry thermometer registers 350 degrees F. Tear off four 24-inch-long sheets of foil; tightly roll each up from a short end to make 4 tubes, about 1/2- inch in diameter. Cut each tube in half with scissors. Loosely wrap a gyoza wrapper around each tube; dab with water to seal the overlapping edge.
Working in two batches, fry the wrappers (on the foil tubes), turning once with tongs, until golden brown, about 1 minute. Transfer to a paper towel-lined plate to drain. Remove the foil tubes from the shells using tongs (the foil will be very hot). Let the shells cool completely.
Mix the goat cheese and ricotta in a small bowl until smooth. Add the olives, fennel seeds, cayenne and a pinch of salt; mix to combine. Transfer the cheese mixture to a resealable plastic bag and snip off a corner. Pipe into the shells from both ends to fill completely. Sprinkle the exposed filling with more chopped olives and pistachios.