Locate and remove any pin bones from salmon flesh. Using sharp
knife, cut flesh off skin, then discard skin. Chop salmon flesh
into 1/4 to 1/3-inch pieces and mix with chopped bread, mayonnaise,
onion, parsley, salt, and lemon juice in medium bowl. Scoop a
generous 1/4-cup portion salmon mixture from bowl and use hands to
form into a patty measuring roughly 2-1/2 inches in diameter and
3/4 inch thick; place on parchment-lined baking sheet and repeat
with remaining salmon mixture until you have 8 patties. Place
patties in freezer until surface moisture has evaporated, about 15
minutes.

Meanwhile, spread flour in pie plate or shallow baking dish. Beat
eggs with 1-1/2 teaspoons vegetable oil and 1-1/2 teaspoons water
in second pie plate or shallow baking dish, and spread bread crumbs
in a third. Dip chilled salmon patties in flour to cover; shake
off excess. Transfer to beaten egg and, using slotted spatula,
turn to coat; let excess drip off. Transfer to bread crumbs; shake
pan to coat patties completely. Return now-breaded patties to
baking sheet.

Heat remaining 1/2 cup vegetable oil in large, heavy-bottomed
skillet over medium-high heat until shimmering but not smoking,
about 3 minutes; add salmon patties and cook until medium golden
brown, about 2 minutes. Flip cakes over and continue cooking until
medium golden brown on second side, about 2 minutes longer. Transfer
cakes to plate lined with paper towels to absorb excess oil on
surface, if desired, about 30 seconds, and then serve immediately,
with the creamy lemon herb dipping sauce, if you like.