1. Using small-whole strainer, drain liquid from Pico de Gallo; discard liquid. Transfer leftover tomato mixture to medium bowl. Mix in black beans, cheese and cilantro until combined.
2. Divide black bean mixture evenly over half of each tortilla (about 1/2 cup each). Fold tortillas in half.
3. Heat large griddle or skillet over medium-high heat. Brush with oil. Place filled tortillas on griddle. Cook, carefully flipping once, until tortillas are golden brown and crisp and cheese filling melts, about 5 minutes.
4. Cut quesadillas into wedges. Serve with Salsita, if desired.