How to Make It
In a blender, puree the tofu with the ketchup, mustard, agave and garlic until smooth. Transfer the sauce to a bowl and stir in the pickle relish and dill; season with salt and refrigerate.
In a large nonstick skillet, heat 2 tablespoons of the oil. Add the onion and cook over moderate heat until lightly browned, 6 minutes. Add the garlic and cook until softened, 2 minutes; season with salt. Scrape the onion and garlic into a food processor. Add the rice, lentils, walnuts, flour and dried basil and pulse until the mixture just comes together and whole grains of rice are still visible; season with salt and pepper. Using lightly oiled hands, press 1/3 cup of the mixture into a 1/2-inch-thick patty; transfer to a plate. Repeat with the remaining mixture for a total of 8 patties.
Wipe out the skillet and heat 1 1/2 tablespoons of the oil in it. Arrange 4 burger patties in the pan and cook over moderately high heat until browned on the bottom, about 5 minutes. Flip the patties and continue cooking until browned and heated through, about 5 minutes longer. Transfer the patties to a work surface. Repeat with the remaining oil and burger patties.
Spread the sauce on 4 of the bun bottoms and top with 4 patties and half of the burger toppings; top with the remaining bun bottoms. Repeat the layering once more, with more sauce and the remaining patties, toppings and the bun tops; serve.