Place red potato cubes into a large saucepan, cover with water, and bring to a boil. Cook potatoes over medium-low heat until tender, about 15 minutes; drain well.

Place chopped cabbage into a saucepan and cover with water; bring to a boil. Reduce heat to medium-low and simmer the cabbage until tender and softened, about 15 minutes; drain well.

Preheat the oven to 375 degrees F (190 degrees C).

Spray a 9x13-inch baking dish with cooking spray.

Lightly toss potatoes, cabbage, corned beef, and Swiss cheese in a large bowl until well combined.

Stir together mustard, white wine, garlic powder, and black pepper in a bowl until smooth; mix into corned beef mixture.

Spread the mixture into the prepared baking dish.

Lay a phyllo sheet onto a work surface and spray with cooking spray. Place the phyllo sheet onto the casserole, folding the overhang back over the dish; spray the dry side of the overhang with more cooking spray.

Repeat three more times, spraying, folding, and respraying the phyllo sheet each time.

Brush the top of last sheet with melted butter.

Bake in the preheated oven until phyllo sheets are crisp and browned and the casserole is hot, 45 to 55 minutes.