1. In a medium bowl, combine tomatoes, onions, parsley, garlic, lime juice, red-pepper flakes, cumin, and 1/4 teaspoon salt. Set aside.Make Quesadillas::
2. Sprinkle both sides of chicken with chili powder, remaining salt, and pepper. Heat 1 tablespoon oil in a large nonstick skillet over medium heat. Add chicken (in 2 batches, if necessary) and cook 3 to 4 minutes per side until golden and cooked through. Transfer chicken to a cutting board and let cool 5 minutes; cut into strips and set aside.
3. Add remaining oil to the same skillet over medium heat. Cook mushrooms, stirring frequently, about 5 minutes or until they have given up their liquid. Transfer mushrooms to a bowl. Carefully wipe skillet clean with a paper towel.
4. Heat skillet over medium heat. Place a tortilla in the skillet. Sprinkle 1/2 cup of cheese and 1/4 of mushrooms over surface of tortilla and continue cooking until cheese begins to melt, about 1 minute. Add 1/4 of chicken over one half of the tortilla. Fold the tortilla in half over the chicken and continue cooking until it is crisp on both sides, about 2 to 3 minutes. Repeat with remaining tortillas, cheese, mushrooms, and chicken. Cut into wedges and serve with salsa.