Grate 1 tsp zest from 2 oranges into a large bowl. Slice peel from top and bottom of oranges. Cut off and discard remaining peel, including white pith, so flesh is showing. Cut out segments over bowl with orange zest. Squeeze leftover orange pulp to extract remaining juice in a measuring cup. Reserve 1/4 cup juice.
Cut leaves from a small head of napa cabbage. Reserve stems for another use. Shred leaves into thin strips. They should measure about 3 cups.
Combine reserved orange juice with orange zest and segments, 2 tsp apple cider vinegar, 1 tsp each finely grated ginger and fish sauce and 1/2 tsp honey in a large bowl. Add shredded cabbage and 1 cup shredded carrot. Toss to coat. Let stand for at least 5 min before serving.