Fill a large pasta pot with water and bring to a boil over medium-high heat. Add the salt and the linguine and cook until al dente, 10 to 12 minutes.
While the water is coming to a boil, add the diced pancetta to a large, deep saute pan. Cook until golden brown and crispy, 6 to 8 minutes. Using a slotted spoon, remove the pancetta to a paper-towel-lined plate to drain. To the same saute pan, add the cream, butter and 1 tablespoon of the black pepper. Bring to a simmer and cook until reduced by a third, about 5 minutes. Stir in the Parmigiano and the Pecorino until smooth; the sauce will be a little thick. Keep warm over low heat.
With tongs, remove the linguine from the pot and add it directly to the sauce; toss along with 1 cup of the pasta cooking water to thin the sauce out. Transfer to a large serving platter and garnish with more Parmigiano and Pecorino, the remaining 1 tablespoon pepper, and the parsley. Taste and adjust the seasoning as needed. Serve immediately.