Melt butter in a skillet over medium heat.
Whisk eggs together with 1 tablespoon of water until light and fluffy. Pour into skillet and cook until eggs begin to set and harden. Pull back the cooked eggs and tilt pan so the uncooked eggs move around and begin to cook too.
Sprinkle on 1/4 cup cheese and then top with a tortilla. Place a plate upside-down over the skillet; flip the skillet over transferring your half done quesadilla to the plate and then back into the skillet again, tortilla side down.
Slice avocado and place onto eggs; sprinkle with remaining cheese, then top off with the other tortilla. Cook for 1-2 minutes. Once again, use the plate to flip over the quesadilla, then slide it back into the skillet with the uncooked tortilla facing down. Cook for 1-2 minutes longer, then remove from the skillet and cut into quarters.
Top with salsa and serve grapes on the side.