In a high-speed blender or food processor, combine cooked split peas, mushrooms, green onions, garlic, flax, soy sauce, lemon, paprika, and pepper. Pulse the mixture 6-8 times or until it sticks together when pressed. Divide into 6 equal parts and roll each into a small fritter the size of a meatball. Use your hands to compress each ball so that they stick together without being held. (don’t be afraid to put a little force into pressing! This will keep them from falling apart during cooking.)
Heat oil in a large skillet over medium-high heat and add fritters to the pan once hot. Leave enough space to easily flip halfway through cooking (cook in batches if you can’t comfortably fit all of the fritters into the same pan at once.) Cook about 4-5 minutes on one side (or until outside is browned and crispy) before carefully flipping and cooking an additional 4-5 minutes. In the meantime, prepare the avocado sauce. Whisk together avocado, lemon, and hot sauce in a small bowl with a fork until smooth. (you can also use a small blender/food processor for this step if desired.) Set aside.
Prepare the sandwiches: slice rolls in half if needed, lay on a flat surface and top with lettuce, tomato, and onion (if using). Once fritters are cooked, divide them between the sandwich rolls and top with spicy avocado sauce to taste. Sandwiches can be prepared in advance and enjoyed hot or at room temperature.