Preheat oven to 425 degrees. Brush tortillas with olive oil. Place on a baking tray; bake until crisp, 8 to 10 minutes.
In a skillet, heat the black beans, liquid and salsa until boiling. Reduce heat to low; simmer, stirring occasionally, until the majority of juice has been absorbed, 5 to 6 minutes.
For the salad, combine lettuce, cubed avocado and crumbled cheese in a bowl. Whisk together lime juice, olive oil, honey, salt and pepper. Pour over salad, then toss until coated.
Top the tortillas with a layer of black beans, then salad. Serve with extra cheese or lime wedges as desired.