In a large skillet, melt 2 tablespoons butter over medium heat.
Add thinly sliced green cabbage and cook until soft and starting to brown, about 10 minutes.
Add mashed potatoes and remaining tablespoon of butter.
Break up any chunks of mashed potato with the back of a spatula. Cook until heated through.
Remove from heat when hot.
Place corn tortillas over flame on a gas stove to heat. Corn tortillas can also be heated in the micorwave. Heat tortillas just until soft and pliable.
Place a heaping tablespoon of the cabbage/potato mixture in the center of each warmed tortilla.
Add a tablesppon of shredded cheese and some sliced green onions.
Fold each filled tortilla in half.
Place a tablespoon of vegetable oil in a shallow skillet and heat over medium high heat.
When oil is hot, fry each tortilla until golden brown and filling is hot and cheese is melted.
Place fried tacos on a plate lined with paper towels to drain.
Sprinkle each taco generously with Parmesan cheese.
Serve tacos with a dollop of sour cream and a side of salsa verde.