Make the Slaw: In a medium bowl, whisk together the mayonnaise, lemon juice, and black pepper until smooth.
Add the coleslaw mix, thinly sliced apple, and green onion.
Toss gently until everything is evenly coated.
Cover and chill in the refrigerator for at least 1 hour to allow the flavors to meld.
Cook the Tempeh: Heat the olive oil in a large nonstick skillet over medium-high heat.
Add the tempeh strips and cook for 3 to 5 minutes, stirring occasionally, until golden brown and slightly crispy.
Stir in the barbecue sauce to coat the tempeh completely, then remove the skillet from the heat.
Warm the Tortillas: Stack the tortillas and wrap them in a slightly damp paper towel. Microwave on high for about 30 seconds, or until they are warm and pliable.
Assemble and Serve: Lay the warm tortillas on a flat surface.
Divide the chilled apple slaw and the warm BBQ tempeh mixture evenly among the four tortillas.
Roll them up, and serve immediately.