Combine the water and 1 teaspoon kosher salt in a medium saucepan and bring to a boil over high heat. Add the broccoli and cook until the broccoli turns bright green and is tender yet crisp, about 1 minute. Drain the water and rinse the broccoli under cold water. Let drain completely and set aside.
Combine the tomato, picante sauce, basil, onion, vinegar, lime juice, garlic, and 1/4 teaspoon kosher salt in a large bowl. Add the broccoli, rice, and cheese and stir to combine. Divide among the tortillas and wrap . Enjoy this wrap immediately.