Blend great Northern beans, 3/4 cup tomatoes, and garlic in a food processor until smooth; add nutritional yeast, cumin, chili powder, salt, and red pepper flakes and blend again.
Transfer bean mixture to a bowl. Stir black beans and 1/4 cup tomatoes into bean mixture.
Heat olive oil in a skillet over medium-high heat.
Place a tortilla in the hot oil. Spread about 1/4 cup filling onto the tortilla.
Place another tortilla on top of filling; cook until filling is warmed, about 10 minutes.
Spray the top tortilla with cooking spray and flip quesadilla to cook the second side until lightly browned, 3 to 5 minutes. Repeat with remaining tortillas and filling.