Heat oven to 300°F (150°C) and place rack in the middle position. Line a rimmed baking sheet with parchment paper.
In a small pot, bring the water to a boil. Add the lentils. Reduce heat to a simmer and cook the lentils for 20 minutes. Drain well.
In a small pot, bring the stock to a boil. Add the quinoa, reduce heat to low, cover, and simmer for 15 minutes. Strain off any remaining water in a fine mesh strainer.
Heat 2 tbsp (30 mL) oil in a medium-size skillet over medium heat. Add the onion and sauté for 3 to 5 minutes or until soft. Add the garlic. Sauté for 1 minute and add the mushrooms, soy sauce, and celery. Cook for 10 to 15 minutes. Drain any residual liquid.
Combine the lentils, quinoa, onion–vegetable mixture, ground almonds, and aquafaba in a food processor. Coarsely grind for 10 to 12 pulses.
Transfer the mixture to a large bowl. Stir in the panko, parsley, and salt.
Divide the mixture into 6 equal portions and pack into four 1-inch (2.5 cm) wide patties. Place on the baking sheet. Bake for 20 minutes.
In a large skillet, heat 2 tbsp (30 mL) oil over medium heat. Lay 4 patties in the pan and cook until crisp and browned on the first side, about 3 minutes. Gently flip the patties and cook until crisp and brown on the other side. Add an extra 1 tbsp (15 mL) oil if the pan is dry.