Season the chicken with the salt and pepper. Whisk together the oil, honey, ginger and garlic. Add the chicken to a baking dish or resealable bag and pour the marinade over top. Refrigerate and marinate for 2 to 24 hours.
When ready to cook, heat a large nonstick skillet over medium heat. Add the chicken (discarding any extra marinade), cover and cook until it is golden brown, about 6 to 8 minutes, stirring once or twice. After the chicken has cooked, you can shred it a bit if desired. (I did.)
To crisp the tortillas, heat a large skillet over medium heat and add the oil 1 tablespoon at a time. Add each tortilla to the skillet and flip, cooking both sides until the are golden and bubbly, about 2 minutes. Remove the tortillas from the skillet and place them on a paper towel to drain.
Assemble the tostadas by adding the chicken on top of the tortilla, adding a sprinkling of green onions and covering with the salsa.