Thinly slice onions, red peppers, and mushrooms. Store in a covered bowl in the fridge. For easier steak slicing, freeze for 15 minutes, then slice and refrigerate.
Melt butter and heat oil in a large skillet. Add sliced veggies and sauté for 3 minutes.
Incorporate sliced steak into the skillet. Season with salt and pepper. Cook for 5-8 minutes. Refrigerate until use.
On one half of each tortilla, distribute cheese, veggie-steak mix, chimichurri sauce, and more cheese. Fold the tortillas.
Melt additional butter in a skillet. Cook quesadillas for 5 minutes each side or until golden brown and cheese is melted.