Using a small-hole strainer, drain liquid from salsa; discard liquid.

Transfer leftover tomato mixture to a medium bowl.

Mix in black beans, cheese, and cilantro until combined.

Divide black bean mixture evenly over half of each tortilla (about 1/2 cup each).

Fold tortillas in half.

Heat large griddle or skillet over medium-high heat.

Brush with oil.

Place filled tortillas on a griddle.

Cook, carefully flipping once, until tortillas are gold brown and crisp and cheese filling melts, about 5 minutes.

Cut quesadillas into wedges.

Serves 8 as a side dish.