In a medium bowl, combine the cucumber, red onion, carrot, cilantro or basil or mint leaves and the rice wine vinegar. Toss well and set aside. This can be made up to 8 hours in advance. Just chop and add the herb leaves last minute to keep them from browning.
Preheat the grill or a large sauté pan over medium high heat. Place the garlic into the bowl of a food processor or blender and pulse a few times to chop it.
Add the green onion and pulse a few times.
Add the salmon to the bowl and pulse a few times to just barely grind it.
Add the sesame oil and soy sauce and pulse a few times just to incorporate the seasonings.
Lightly oil the grill with a thin coating of vegetable oil or spray the sauté pan with a little cooking spray. Divide the salmon mixture into 4 patties and place gently onto the grill or into the sauté pan. Allow the burgers to cook for about 6 minutes per side and don’t move them around too much.
While the burgers are cooking you can spread the hoisin sauce on the inside top of each bun and divide the lettuce between the top buns. Once the burgers are cooked, place them onto the bottom buns and top with the cucumber and carrot mixture, them place the top bun with the lettuce on top. Enjoy them hot off the grill.