Generously butter a 4-quart baking dish. Peel the potatoes and cut into chunks. Bring a large pot of water to a simmer and add the potatoes. Bring to a boil and cook until fork-tender, 20 to 25 minutes.
Heat 1/2 inch vegetable oil in a large pot over medium-high heat. Working in batches, fry the shallots until they are slightly golden, 3 to 4 minutes. Remove with a slotted spoon and drain on paper towels.
Drain the potatoes in a large colander. Place them back in the dry pot and put the pot on the stove. Mash the potatoes over low heat, allowing all the steam to escape before adding in the other ingredients. Turn off the heat and add 1 1/2 sticks butter, the cream cheese, heavy cream, seasoned salt, 1/2 teaspoon kosher salt and 1 teaspoon pepper. Mash to combine.
Preheat the oven to 350 degrees F. Spread three-quarters of the shallots in the bottom of the baking dish. Scoop the mashed potatoes on top and spread them over the shallots. Sprinkle the remaining shallots on top of the potatoes.
Cut the remaining 1/2 stick butter into pieces and sprinkle over the potatoes. Bake until the butter is melted and the potatoes are warmed through, 25 to 30 minutes.
The potatoes can be made a day ahead through the end of step 4; cover and refrigerate. Before serving, dot with butter and bake for an hour.