Soak the almonds in 1 cup water for 1 hour at room temperature.
Meanwhile, in a small saucepan, bring the quinoa and 1 cup water to a boil. Cover, reduce the heat to very low and cook until tender, about 15 minutes. Let cool in the pan uncovered, stirring occasionally. Transfer to a large bowl.
Drain the almonds, reserving the soaking liquid. Using a food processor, grind the almonds with 1 tbsp. EVOO, the lemon juice, garlic, 3/4 tsp. salt and 1/4 tsp. pepper. With the machine on, pour in 3/4 cup of the reserved soaking liquid and process until smooth; season to taste.
In a medium skillet, heat 1 tbsp. EVOO over medium-high heat. Add the onion and cook, stirring, until caramelized, about 5 minutes. Add the mushrooms, reduce the heat to medium and cook until browned, about 5 minutes.
Stir the onion-mushroom mixture into the quinoa. Add the beans and mash the mixture with your hands until most of the beans are broken down. Stir in the cereal, sunflower seeds and ketchup; season with salt and pepper. Shape the mixture into four 4-inch patties.
Preheat a well-oiled grill to medium. Grill the burgers, carefully turning once, until crusted on both sides, about 5 minutes.
Slather all of the bread slices with the almond sauce. Place a veggie burger on top of 4 of the slices. Top with the tomato, sprouts and remaining bread slices.