Place the potatoes in a large pot of boiling water. Cover and boil for 20 minutes. Drain and return to the pot.
Add the salt, pepper, butter, sour cream, and egg to the potatoes and mash until desired consistency is reached. Set aside.
Heat the remaining butter in a large skillet over medium heat.
Add in the cabbage, onion, and garlic. Saute for 10 minutes. Remove from heat and stir in the chicken bouillon cubes, stirring until they dissolve.
Add the cabbage mixture to the potato mixture and mix until combined.
Preheat the oven to 375 degrees.
Pour the potato and cabbage mixture into a large baking dish. Bake for 20 minutes.
Remove from oven and sprinkle with the Skellig and Dubliner cheeses. Return to oven and continue baking for 10 minutes.
Serve hot.