Peel the potatoes and cut into equal size chunks. Peel the carrot and them into equal size chunks but smaller than the potatoes.
Place the potatoes and carrot in a large pot and cover with water. Add in 1/2 tablespoon salt, cover and bring it to a boil. Lower the heat to a simmer and cook until the potatoes and carrot are very soft.
Drain the potatoes and carrot (discard the water) and pour the potatoes and carrot back into the pot. Turn the heat down to the lowest possible and place the pot on top. Working quickly, mash the potatoes and carrot over low heat. This will allow the excess moisture to evaporate. You can mash 90% and leave 10% in small chunks (personal preference).
Once the potatoes and carrot have been mashed, remove from heat and add in butter, cheese, cream/milk and stir until all are mixed together. Season with salt and black pepper, starting with a little at first, and work your way up from there, tasting all the time. Whisk a little more vigorously to ensure all the seasonings are evenly distributed.