In a small bowl, whisk together soy sauce, honey, peanut butter, rice vinegar, sesame oil and water.
Spread enough of the peanut sauce on each flatbread to cover the surface. You want there to be enough left to drizzle some on the cooked flatbreads.
Evenly divide the cheese between the two flatbreads, followed by the broccoli, carrots and green onions. Place flatbreads on a baking sheet and cook until cheese is bubbly and hot, about 12-15 minutes.
Sprinkle with chopped cilantro and peanuts. Drizzle with more peanut sauce.