1. Grate the Chihuahua cheese. If you have no Chihuahua, a mild cheddar or other good melting cheese works well.
2. Lay out four flour tortillas, sprinkle each with half the cheese, lay the ham slices on top and cover with the rest of the cheese.
3. Place a second tortilla on each and press down lightly.
4. Lightly oil a large frying pan and cook the sincronizadas one at a time over medium heat for 2-3 minutes per side until golden and the cheese has melted; turn with a wide spatula.
5. Meanwhile, mash the avocado with a fork, lime juice and a pinch of salt.
6. Cut the sincronizadas into quarters and serve with the avocado cream and perhaps some salsa.
Tip: It's not the same as a quesadilla: a sincronizada is a "sandwich" between two tortillas – the name means "synchronised", because both sheets cook together.
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