Bring a large pot of lightly salted water to a boil. Add penne and cook, stirring occasionally, until tender yet firm to the bite, 10 to 11 minutes. Drain.

Heat oil in a skillet over medium heat; stir in onion and garlic. Cook and stir until the onion has softened and turned translucent, about 4 minutes. Add pancetta and prosciutto; saute until crisp and brown, about 8 minutes. Add chicken and saute until heated through, about 2 minutes. Remove from the heat and set aside to cool slightly.

Whisk cream, Parmigiano-Reggiano cheese, egg yolks, basil, and parsley together in a large bowl until blended.

Return chicken mixture to the stove over medium-low heat. Add drained penne and cream mixture; toss over medium-low heat until penne is thickly coated, about 4 minutes; do not let it boil or the eggs will scramble. Taste and season with salt and pepper if necessary.