Scramble the eggs.  Break the eggs into a small mixing bowl and whisk or beat with a fork.  Heat a small nonstick pan over medium-low heat.  Add the eggs and cook, stirring frequently, until they are cooked through.  

Mash the avocado.  Cut the avocado in half and remove the pit.  Remove the skin from the flesh and add to a small bowl.  Add the lime juice and mash with a fork until combined.  

Assemble the quesadilla.  Lightly brush a non-stick pan with olive or avocado oil.  Heat over just below medium heat.  Add one tortilla to the pan.  Top with half of the eggs, half of the avocado mixture and sprinkle with half of the cheese.  Top with chopped cilantro.  Add a second tortilla on top.

Cook the quesadilla.  Cook for 3 minutes or until the tortilla is a nice golden brown color.  Carefully flip the quesadilla and continue cooking for another 2-3 minutes, until the second tortilla is golden brown.  Remove from the pan and repeat with the remaining ingredients.  

Serve.  Cut each quesadilla into pieces and serve immediately.