Clean and remove stems from your kale leaves, then roughly chop them up.
Fill a medium saucepan with a few inches of water and place it over high heat. Place your kale into a steamer basket. Once the water comes to a boil, lower the heat so that the water is simmering, place the steamer basket into the pot, and cover. Steam the kale until wilted, about 4 minutes (Note 1).
Place kale leaves into a large food processor bowl fitted with an s-blade, along with the beans, breadcrumbs, sunflower seeds, basil, garlic, lemon juice, salt, and pepper.
Run the machine briefly, then stop to scrape down the sides of the bowl and redistribute the ingredients with a rubber spatula. Repeat this until the ingredients are finely chopped and well combined, but the mixture still has some texture (Note 2). Taste-test the mixture and add more salt and pepper, if desired.
Shape the mixture into 4 to 6 patties.
Lightly oil the bottom of a medium skillet and place it over medium heat. Working in batches if needed, place the patties into skillet and cook them for 4 to 5 minutes on each side, until browned.
Stuff the patties into buns and top with toppings of choice. Serve.