Preheat the oven to 350°F (175°C).
Wash and peel the Yukon Gold potatoes. Cut them into thin, even slices (about ¼ inch thick).
In a large pot, bring salted water to a boil. Add the sliced potatoes and cook for 10-12 minutes until they are just tender but not falling apart. Drain and set aside.
In a mixing bowl, combine the heavy cream, melted butter, minced garlic, salt, black pepper, and paprika. Whisk until well blended.
In the same bowl, fold in the shredded sharp cheddar and mozzarella cheeses, saving a little cheese for the topping.
Layer half of the cooked potatoes in the baking dish. Pour half of the creamy cheese mixture over the potatoes. Repeat with the remaining potatoes and cheese mixture.
Top with the reserved cheese. If desired, sprinkle a little extra paprika on top for added flavor.
Cover the baking dish with aluminum foil and bake in the preheated oven for 30 minutes.
After 30 minutes, remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden brown.
Once done, remove from the oven and let it cool for a few minutes. Garnish with chopped green onions before serving.