Fry the shallots (optional). Add the sliced shallots and neutral oil to a cold medium saucepan. Heat over medium heat, stirring occasionally, for 10–12 minutes until pale golden. Scoop out onto a paper towel-lined plate using a slotted spoon, season immediately with salt, and set aside.

Boil the potatoes. Place the potato chunks in a large pot and cover with cold water by 1 inch. Add 1 tablespoon of kosher salt, bring to a boil, and cook uncovered until fork-tender (12–15 minutes).

Drain the potatoes well, then return them to the warm pot over low heat for 1 minute to cook off excess moisture.

Rice or mash the hot potatoes until smooth.

Using a spatula, fold in the Toasted Onion Dip, softened butter, and grated Parmesan until silky and fully combined.

Stir in warm heavy cream or milk a couple of tablespoons at a time until you reach your desired texture. Season with kosher salt to taste, starting with 1/2 teaspoon.

Transfer the potatoes to a serving dish and top with fresh chives and crispy shallots if using.