Preheat the oven to 350°F. Line a baking sheet with parchment paper. Grease 6 cups of a standard muffin tin with olive oil and set aside.
Scatter the drained white beans over the lined baking sheet in an even layer. Bake the white beans in the oven for 13-15 minutes, or until beans are slightly dried and starting to break up. Let them cool.
Set a medium sauté pan over medium heat. Pour in 1 tablespoon of the olive oil and swirl it around. Add the onions, celery, carrot, and garlic to the pan all at once. Stir and sauté the vegetables until all are soft and translucent, about 8-10 minutes. Season with salt and pepper. Pour in the white wine vinegar and let it cook off for 30 seconds or so. Remove from the heat and allow the sautéed vegetables to cool slightly.
In a food processor or small food chopper, pulse the walnut halves into a coarse meal. Pour the walnut meal into a large mixing bowl. Then, transfer the oven-dried white beans to the food processor. Pulse the white beans to grind them up. They should have a wet sand-like texture with a few whole pieces of bean still in the mix. Transfer the ground white beans to the large mixing bowl with the walnuts.
To the white bean and walnut mixture, add the cooled sautéed vegetables, the sweet potato purée, 2 tablespoons of the hot sauce, tomato paste, tamari, smoked paprika, garlic powder, onion powder, and the remaining tablespoon of olive oil. Season the mixture liberally with salt and pepper. Using a spatula, mix thoroughly until everything is evenly combined and smooth.
Divide the spicy vegan buffalo meatloaf mixture among the greased muffin cups. I like to smooth the tops and shape them like a dome. In a small bowl, stir together the remaining hot sauce and ketchup. Brush this mixture over the entire surface of the mini meatloaves.
Bake the spicy vegan buffalo meatloaf minis until the loaves are firm and the ketchup glaze is caramelized, about 27-30 minutes. Serve warm with side dishes of your choosing.