Brown the beef and onion in a large skillet over medium-high heat for 7 to 8 minutes, breaking the beef into small crumbles and cooking it to 160°F. Drain excess fat.
Stir in cumin, chili powder, salt and water. Simmer for 2 minutes until the meat is moist but no free liquid remains, then transfer to a bowl.
Scatter half the cheese over one half of each tortilla. Divide the beef over the cheese, add the remaining cheese and fold the bare tortilla halves over.
Wipe the skillet and brush with 1 teaspoon oil. Cook two folded quesadillas over medium heat for 2 to 3 minutes per side until golden; repeat with the remaining oil and quesadillas.
Rest for 1 minute before cutting into wedges. Divide the salsa and sour cream among four servings.