Heat the oven to 200°C/400°Whisk together the ketchup, vinegar, brown sugar, soy sauce, vegetable oil, smoked paprika and garlic. Place the mushrooms on a baking sheet lined with baking paper. Brush over the sauce and place in the oven, cook for 30 minutes.
Mix together all of the slaw ingredients and set aside.
When the mushrooms have finished cooking use 2 forks to shred them, drizzle over a little more sauce and toss. Serve in rolls with slaw.
Nutrition information is an estimate and will vary depending on the exact ingredients used.