The first thing that comes to my mind, when dealing with leftovers, is soup. You can make a soup out of just about anything you have on hand, including holiday leftovers.
This year we didn’t have turkey for Christmas, we had  Roasted Chickens instead. After pulling off the meat, I kept the carcass to make our soup of the week. I’ll add them to 4 quarts of water with a teaspoon of salt, 2 celery stalks, 1 medium onion and 2 carrots. I’ll bring the mixture to a boil, then turn the heat down, allowing it to simmer for an hour or so, then drain off the broth, to use for the soup stock. I’ll reserve any loose chicken meat and the vegetables.
To the stock, I’ll add back in the carrots, celery, onion* and any leftover chicken, vegetables, including the mashed potatoes and gravy. The potatoes will thicken the soup and give it a creamy texture. Taste to see if it needs more seasonings, then simmer for 10 to 15 minutes, giving the ingredients time to mingle. Serve the soup with a loaf of warm French Bread and a new dessert. No one will know they are eating what was left of their holiday feast.
My second suggestion is a frittata. It’s another easy dinner that can utilize a lot of the stuff you might otherwise have thrown away.
To make one, use two or three eggs per person. Crack into a bowl and beat with salt and pepper. Then, add in vegetable leftovers, using whatever is in the fridge. Cold meat, can be sliced into bite size pieces and added in. Cooked vegetables can go right in. You may want to rinse them in hot water to remove their older seasonings. If so, be sure to drain them well before adding them to the egg mixture or your frittata might become wet and runny.
Firm fresh produce (carrots, broccoli, and even mushrooms) should be sauteed until tender, preferably with a little garlic or onion, before adding to the eggs. Italians even throw in leftover pasta, which is a great way to use those leftovers. Then, heat a little olive oil in a large saute pan, that can also be used in the oven and pour in the egg mixture.
While the egg mixture is cooking, turn the broiler on low. Heat eggs on stove top until they start setting around the edge of the pan. Then, grate some cheese over the top. (Use what you have on hand. Cheddar is really good with broccoli; Italian cheese like Parmesan is delicious with ham and/or mushroom.) Turn off the stove top and place the pan under the broiler until eggs are set and cheese is melted. Allow to cool briefly, then slice as you would a pie and serve.
You have just made good use of food items that might have gotten tossed. In turn, you have a couple of delicious dinners and saved lots of money in your food budget using your leftovers.
* cut the vegetables into 1/2 inch pieces