Do a fondue.
3/4 cup milk
3/4 cup apple juice, or cider
1/4 cup all-purpose flour
1 tbsp Dijon mustard
1 tsp salt
1/4 tsp black pepper
2 cups shredded sharp cheddar
French bread, cut into cubes
lightly steamed vegetables, cut into chunks
In a medium saucepan, whisk together the milk, apple juice, flour, mustard, salt and pepper. Place over medium heat and cook, stirring, until the mixture comes to a boil and thickens. Let simmer for about a minute, then remove from heat. Add the shredded cheese by handfuls, stirring between each addition, until all the cheese is melted and the mixture is smooth. Transfer to a fondue pot over a flame and serve with bread cubes and vegetables for dipping.