Prep: Preheat the oven to 425F and set a baking sheet aside. Bring ~4 cups of water to a boil, then carefully pour over (or add in) the soy curls and soak for 5 minutes. Drain the soy curls well, pressing or squeezing out as much water as possible.
Vegetables: Add the corn, sweet potato, red cabbage, paprika, cumin, garlic, salt, and oil to a large bowl. Mix well, then transfer to the baking sheet, spreading the vegetables out evenly across 2/3 of the sheet.
Soy Curls: Add the rehydrated soy curls to the same bowl with 1/2 cup (120 ml) of the BBQ sauce and oil. Mix well, then transfer to the other 1/3 of the baking sheet and spread out evenly.
Bake: Bake on the top rack of the oven for 20 minutes, then quickly remove and flip the vegetables and soy curls, keeping them separate. Return to the oven and bake for an additional 10 minutes, until the soy curls begin to crisp up around the edges.
Garnish and Serve: Remove the baking tray from the oven and toss the soy curls with the remaining BBQ sauce. You can mix everything together at this point, or keep it separate for serving. Garnish with sliced green onions and serve warm. Leftovers will keep in the fridge for up to 5 days.