Preheat oven to 425F.
Make the mashed potatoes. In a large pot, cover the chopped potatoes with cold water until covered. Add 2 hefty pinches of kosher salt. Bring to a light boil, cook uncovered for 15-20 mins till fork tender. Drain, then add butter and milk or sour cream and mash until combined. Set aside
Heat the olive oil over medium heat in a deep cast iron (or oven-safe) skillet. Add the onion and garlic, sauteing for 3-4 mins. Add the five spice and saute until fragrant.
Push the onions to the side of the pan and add the mushrooms. Drizzle with more olive oil and saute for 3-4 mins. Add the lentils, gochujang and soy sauce then toss to combine. Stir in the vegetable stock and season with a pinch of kosher salt and sugar. Bring to a rapid simmer and cover. Cook for 10 mins. Taste and adjust seasoning if needed.
Remove from heat, and spread mashed potatoes on top. If using a non-oven-safe skillet, transfer lentils to a baking dish then proceed.
Bake for 10-15 mins until potatoes are lightly browned.
Let cool to thicken then garnish with parmigiano reggiano and fresh chives.
