To make the meatballs, heat the oil in a large skillet over medium heat. Add the eggplant, onion, and salt. Cook, stirring occasionally, for 15 to 20 minutes, until the eggplant is translucent and very soft. Add garlic in the last couple of minutes of cooking. Remove from heat and set aside.
Preheat the oven to 190°C/375°F/gas mark 5. Line a baking tray with parchment paper. If you have a small food processor, this next step should be done equally in two batches. In a food processor, pulse together the oats, 1 cup of breadcrumbs, walnuts, salt, allspice, nutmeg, and black pepper. Add the white beans and process until combined. Transfer the eggplant to the food processor, scraping in any brown bits in the pan, and pulse until everything is combined. The mixture should be fairly well-blended but retain some texture. Set the pan aside for making the gravy.
Spread two tablespoons of oil on the parchment. Place the remaining 1 cup of breadcrumbs in a small bowl. Using a tablespoon or portion scoop, shape the mixture into balls approximately 1½ inches in diameter. Roll each one in breadcrumbs and arrange on the baking tray. Bake for about 30 minutes, until the meatballs are firm and crispy on the outside.
While the meatballs are baking, make the gravy. Melt the butter in the eggplant pan. Whisk in the flour and cook for 3 to 4 minutes. Whisk in the broth and stir until smooth and thickened. Stir in nutritional yeast, tamari, Worcestershire sauce, mustard, pepper, and salt. Gently simmer over medium-low heat until the gravy thickens, about 5 minutes. Stir in yogurt. Taste and add more salt if you like. Transfer meatballs to the pan and spoon gravy over them. Cook gently for about 5 minutes. Transfer to a serving dish, sprinkle with parsley and serve.