Begin the recipe by opening the 14 ¾ ounce can of pink salmon and drain off the salmon juice liquid. You can discard the liquid as you will not need it for later. Place the pink salmon into a large bowl and use a fork to separate and mash it into smaller pieces.
To the same mixing bowl, add the ½ cup chopped onion, 1 tablespoon chopped fresh parsley, ¼ teaspoon salt, ¼ teaspoon ground black pepper, and 1 tablespoon lemon juice. Stir to combine.
Add the 1 large lightly beaten egg and stir to combine. The mixture will be slightly sticky at this point. Add the ¾ cup breadcrumbs and stir to combine. The salmon mixture should be sticking onto itself.
Now it's time to form the patties into round even sized circles similar to a hamburger patty, they should look like salmon burgers.
Place a large skillet on the stovetop over medium-high heat. Once heated add the 3 tablespoons oil and allow it to heat thoroughly. Add in the patties and be sure not to crowd the pan so they cook evenly and fry up crispy. After 2 to 3 minutes, flip each patty over to the opposite side and continue cooking for an additional 2 to 3 minutes until golden brown.
Carefully remove each patty from the skillet using a spatula and place it on a paper towel lined plate to absorb the excess oil. Continue the process with the other patties until finished.
If you need to add more oil, then do that once you remove the patties from the skillet and before adding the next batch. Once you have cooked all of the salmon patties, serve them warm, and enjoy!