Layer on half of each tortilla: 1/4 cup cheese, 2 tablespoons diced tomatoes. 1 tablespoon bacon and 1 tablespoon basil. Fold each tortilla in half to form a half circle.
Lightly coat a large nonstick skillet or griddle with oil. Cook each quesadilla, over medium-high heat for 1 1/2 minutes on each side until cheese is melted and tortilla is lightly browned.
Cut the quesadilla into 4 wedges and serve with sour cream.