In a mixing bowl, combine the diced large tomato, chopped red onion, and fresh spinach. Squeeze out any excess moisture from the spinach. Add crumbled feta and shredded mozzarella cheese, along with dried oregano. Mix gently until evenly distributed.

Lay out three 8-inch flour tortillas on a clean surface. Place about 1/3 cup of the filling on one half of each tortilla. Fold the untopped half over the filling and press down gently.

Heat a non-stick skillet over medium heat and drizzle with oil. Once hot, place the folded quesadillas in the skillet. Cook for 3 to 4 minutes until the bottom is golden brown and the cheese begins to melt. Flip and cook the other side for an additional 3 to 4 minutes.

Transfer the quesadillas to a cutting board and allow to rest for about 1 minute. Use a knife to cut each quesadilla into triangles. Serve warm.