Notes: This salad is adapted from one served by executive chef Mark Dommen of Julia's Kitchen at Copia in Napa, California. Small squid (also called calamari) are frequently sold cleaned as tubes (mantles), tubes and tentacles, or rings (sliced tubes). Sometimes a few pieces slip through without thorough cleaning. Check whole tubes and pull out and discard any long, clear quills; squeeze out and discard material in tubes. You can prepare salad through step 4 up to 1 day ahead; cover and chill ingredients separately.
1 pound cleaned squid (calamari; see notes) or bay scallops
In a 5- to 6-quart pan over high heat, bring 2 1/2 to 3 quarts water to a boil. Meanwhile, if necessary, cut squid tubes crosswise into 1/4-inch-thick rings; leave tentacles whole. Rinse and drain squid or scallops.
Stir squid or scallops into boiling water; cover tightly and remove from heat. Let stand just until squid feels firm when pressed, about 1 minute (do not overcook or squid may turn rubbery), or scallops are barely opaque but still moist-looking in the center (cut to test), about 2 minutes. Drain, rinse in cold water, and drain again thoroughly. Pour the seafood into a large bowl.
Cut and discard peel and white membrane from oranges. One at a time, hold oranges over a bowl and cut between membranes and fruit to release segments into the bowl. Squeeze juice from membranes into the bowl; discard membranes.
Pour orange segments and juice into a wire strainer set over a 1- to 1 1/2-quart pan. Reserve segments. Bring juice to a boil over high heat and boil, stirring occasionally, until reduced to 2 tablespoons, 2 to 6 minutes. Remove from heat. Stir in oil, lime juice, shallots, ginger, sugar, and salt and pepper to taste.
Add orange dressing, orange segments, lettuce, jicama, and mint to squid; mix gently. Add more salt and pepper to taste. Divide mixture evenly among four dinner plates.