Reheating mashed potatoes in the oven or on a hob gives you more options than using the microwave. It also greatly simplifies your cooking routine if you can make mashed potatoes ahead of time, freeze or refrigerate and then simply reheat the mash. When preparing mashed potatoes that you plan on reheating, use a lower-starch potato to keep the mash firm. Whether you use the hob or oven depends on the results you want, how much time you want to spend and the ingredients and cookware you plan to use.
On the hob
Mix additional liquid such as chicken stock or milk into the potatoes to reconstitute them. They tend to dry out when refrigerated or frozen. Stir in a little more liquid than you feel necessary to produce potatoes with a loose consistency.
Transfer the potato mixture to a non-stick saucepan and turn the hob to a low-medium heat. Stir the potatoes with a wooden spatula while heating to ensure that they heat uniformly. Add more liquid if necessary.
Sample your mash for flavour and texture. If you want mashed potatoes with a fluffier consistency, mash them again with a mixer or whip them. Even if you want denser mashed potatoes, you will probably need to re-mash them with a hand masher or spoon.
In the oven
Preheat your oven to 180 degrees C (350F) and transfer the potatoes to a baking or casserole dish.
Add extra liquid into the potatoes and stir until the consistency is uniform. If desired, add additional spices or mix or sprinkle cheese on top.
Cover the dish with aluminium foil and bake for half an hour. Check the consistency halfway through reheating and add more liquid if needed.
When reheating in the oven, you can make cheese or au gratin potatoes by mixing an egg and some milk into the potatoes and covering with cheese.