Stir together chicken, black beans, salsa, cilantro, chili powder, cumin and shredded Monterey Jack cheese in medium bowl. Divide mixture equally onto one side of each flour tortilla; fold tortilla in half over filling.
Melt 1 tablespoon butter in 12-inch nonstick skillet over medium heat. Cook two quesadillas at a time 4-6 minutes, turning once, until light golden brown. Repeat with remaining 1 tablespoon butter and remaining two quesadillas.