Fried Potato Casserole

2 russet potatoes •

5 med. Yukon Gold potatoes •

26-28 small purple potatoes (approx. 1 lb.) •

1 med. sweet potato •

1/4 cup extra virgin olive oil •

3 cups half-and-half, used separately •

1 teaspoon coarse salt •

1 teaspoon freshly-ground pepper •

2 tablespoons flour •

1/2 cup grated gruyere cheese •

1 cup grated cheddar cheese •

1 cup grated gouda cheese