Heat 1 ½ Tablespoons of the olive oil in a medium skillet over low heat.
Add the onion and cook until soft and translucent, about 10 minutes.
Add the honey and vinegar and cook until onion is caramelized and liquid has mostly evaporated.
Transfer the onion mixture to a bowl and set aside.
In the same skillet, add the remaining 1 ½ Tablespoons of oil and the butter.
Add the mushrooms and sauté until mushrooms start to release juices.
Add the garlic and cook mixture until mushrooms have completely softened.
Season with salt and pepper.
Remove pan from the heat and set aside.
Heat a large pan or griddle over medium-high heat.
One at a time, lightly toast all the tortillas on one side for a minute and set aside.
Align 4 tortillas side by side toasted side up.
Top each tortilla with cheese, onion, mushrooms, ⅛ of the chopped arugula, and finishing with more of the cheese.
Top each filled tortilla with the remaining tortilla, toasted side down.
Add a little olive oil to pan or griddle and cook each side for 3 to 4 minutes per side or until cheese is melted.
Cut tortillas into quarters (or eighths for smaller pieces) and sprinkle some chopped arugula on top.
Serve with a dollop of sour cream.