Put the potatoes in a large saucepan, add cold water cover by at least an inch, 1 tsp. salt, and bring water to a boil over high heat. Cover the pan, reduce the heat to medium to maintain a steady (not raging) boil, and cook until the potatoes are tender all the way through but don’t fall apart when pierced with a fork, about 20 minutes.
Meanwhile, heat the corn oil in a medium saucepan over medium-high heat. Add the split peas and cook just until they start to turn golden brown (watch carefully: split peas can quickly go from golden brown to dark brown to burned), about 3 minutes. Add the cumin seeds and cook, stirring, for 30 seconds. Add the butter, onion, and turmeric and cook until the onion is transparent, 4 to 5 minutes. In a small bowl, whisk the honey and mustard powder until smooth. Stir in the milk and cream and then add this mixture to the onions and spices. Reduce the heat to low and simmer for 5 minutes. Turn off the heat, cover the pan, and let it sit on the burner.
When the potatoes are tender, drain them and return them to their saucepan over medium heat. Dry the potatoes, shaking the pan and stirring with a rubber spatula, until they look floury and leave a light film on the bottom of the pan. Put the dry potatoes through a ricer or food mill, or mash them with a hand masher until they’re lump-free.
Pour the hot creamy onion mixture into the pan with the warm mashed potatoes. Stir slowly with a wooden spoon to thoroughly combine. If the potatoes seem dry, moisten with a little more milk. Transfer the spiced mashed potatoes to a serving bowl. Season with salt and pepper to taste. Serve at once.