Make the sauce by combining tofu, ketchup, mustard, agave and garlic in a blender until smooth. Stir in pickle relish and dill. Season with salt and pepper and refrigerate.
Scrape onion/garlic mixture into a food processor and add rice, lentils, walnuts, four and basil and pulse until combined (but grains are still visible).
Using lightly oiled hands, make 1/2 inch thick patties with 1/3 cup of the mixture until mixture is gone (should make 8 patties).
Wipe out skillet and heat 1 1/2 tablespoons of oil in it. Fry patties in batches over moderate heat until browned (5 minutes on each side)
To assemble the burgers, spread sauce on the bottom of a toasted bun, top with a patty, veggies and burger bun (or add an extra patty for a double!).