Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Put the potatoes in large saucepan, cover with cold water by about 1 inch and add 2 tablespoons salt. Bring to a boil, uncovered, over high heat, and then reduce the heat to medium-high and simmer briskly until fork tender, about 45 minutes. Drain the potatoes, reserving 3/4 cup of the water. Quarter the potatoes and pass them through a food mill or ricer back into the pan. (Peel the quarters first if you are using a ricer).
Lay the pancetta in a cool skillet and render over medium-high heat until crisp, about 8 minutes. Drain, reserving the fat, and chop into bits.
Fold in 1/4 cup reserved pancetta fat, pancetta bits, Pecorino and reserved cooking water into the potatoes. Season with salt. Fold in 4 egg yolks until well blended. Spoon or pipe six 1-cup mounds onto the prepared baking sheet and top with pepper. Make little wells in each mound with the back of a spoon. Bake until the edges are golden brown, about 15 minutes. Remove from the oven, fill each well with one of the remaining 6 yolks and place back in the oven to lightly cook the yolk, 2 to 3 minutes. Serve immediately.