Preheat oven to 350 degrees. Line a baking sheet with parchment paper. Arrange tortilla strips in a single layer. Bake for 10 to 12 minutes, checking towards the end to avoid burning.
Meanwhile, in a large bowl combine quinoa, pinto beans, chopped tomato, corn and red onion. Add lettuce or mixed greens if serving immediately. (Otherwise wait to add the greens until you toss and serve.)
In a small bowl combine veganaise, milk, barbecue sauce, onion powder, garlic and parsley. Whisk well until smooth.
Toss ¾ of dressing with quinoa mixture and lettuce. Drizzle with additional dressing or barbecue sauce as desired.