Place the potatoes in a large pot of salted cold water. Bring to a boil, then reduce to a simmer and cook until fork-tender, about 15–18 minutes. Drain well and return to the pot.
While the potatoes cook, melt 1 tablespoon of butter in a large skillet over medium heat. Add the pancetta and cook until crispy, about 5–6 minutes. Remove the pancetta with a slotted spoon and set aside on a paper towel–lined plate.
In the same skillet with the pancetta drippings, add the remaining 2 tablespoons of butter. Add the cabbage and kale with a pinch of salt and cook, stirring occasionally, until the greens are tender and just starting to turn golden, about 6–8 minutes.
Mash the potatoes with the sour cream and warm milk until smooth and creamy. You want them fluffy but not gluey — don't overwork them.
Fold the sautéed cabbage and kale into the mashed potatoes along with most of the chives. Season generously with salt and pepper.
Transfer to a serving bowl and top with the crispy pancetta, remaining chives, and a pool of melted butter in the center if you're feeling traditional.