Combine the ingredients for the salmon cakes; breadcrumbs through black pepper in a medium bowl and mix well.
In the bowl of of a food processor, pulse 1/3 of the chopped salmon 2 or 3 times or until they are about 1/4" pieces. Don't over process the fish, not all the pieces will be even, but they should be mushy.
Transfer the processed salmon into the bowl with panko mixture, and continue processing the 2 batches of remaining salmon, one at a time.
Once all the salmon has been processed, gently mix with the panko mixture until evenly distributed.
On a parchment lined baking sheet, measure out 8 salmon cakes using a 1/3 cup measuring cup.
Place 3/4 cup panko bread crumbs in a pie plate or dish. Coat each salmon patty with bread crumbs, forming them into patties about 1" by 2 1/2".
In a large skillet, heat oil until shimmering over a medium high heat. Fry cakes about 2 minutes. Carefully flip salmon cakes and fry an additional 2-3 minutes or until deep golden brown.
Transfer salmon cakes onto a paper towel lined plate. Serve immediately with lemon wedges.
Store any leftovers in an airtight container for no more than 1 day.