Bring a large pot of salted water to a boil. Add bucatini and cook al dente, about 9-10 minutes. Drain, reserving 3 tablespoons of the cooking water.
Meanwhile, in a large skillet set to medium-low heat, add oil. Add diced pancetta and cook 'til crisp, 5-7 minutes. Add shallot and garlic, cooking for 1 minute. Add heavy cream. Simmer until slightly thickened, about 2 minutes.
Add hot pasta to the skillet and stir to coat. Remove from the heat.
Stir in the reserved pasta cooking water, grated cheese, and egg yolks.
Divide pasta into bowls and sprinkle with parsley, pepper, and additional cheese. Serve warm.
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