Place cashews in a bowl with water to cover by 1 inch. Let stand 8 hours or overnight.
Preheat oven to 450°F. Line a 13- x 9-inch baking dish with aluminum foil. Trim ends from carrots to fit hot dog buns. Using a vegetable peeler, peel carrots, and round edges to create a hot dog shape.
Place oil, tamari, liquid smoke (if desired), paprika, garlic powder, and onion powder in a small bowl. Stir with a whisk. Place carrots in a single layer in prepared baking dish. Pour oil mixture over carrots; rub to coat on all sides. Bake at 450°F for 35 minutes, tossing every 15 minutes.
Drain cashews. Place cashews, jarred salsa, almond milk, yeast, cayenne pepper, cumin, turmeric, and salt in a high-powered blender. Process until creamy, 2 to 3 minutes. Stir in up to 1 tablespoon water, 1 teaspoon at a time, until desired consistency is reached.
Place 1 roasted carrot in each bun. Top each with 2 tablespoons nacho sauce; top evenly with jalapeño slices and diced red onion.