In a skillet over medium heat, add the olive oil. Once hot, add the minced garlic and sauté for about 30 seconds until fragrant.
Add the cleaned and trimmed squash blossoms to the skillet. Season with salt and black pepper. Sauté for 3-4 minutes until the blossoms are tender. Remove from heat and set aside.
In a separate skillet, heat a little oil over medium heat. Place one tortilla in the skillet and sprinkle with a generous amount of shredded Oaxaca cheese.
Top the cheese with a portion of the sautéed squash blossoms, then place another tortilla on top. Cook for about 2-3 minutes until the bottom tortilla is golden brown and the cheese begins to melt.
Carefully flip the quesadilla and cook for an additional 2-3 minutes on the other side until golden brown and crispy. Remove from the skillet and let it cool slightly before cutting into wedges.
Repeat the process with the remaining tortillas, cheese, and squash blossoms.
Serve warm, garnished with fresh cilantro and accompanied by sour cream or salsa if desired.