Fill a large pot with water and bring to a boil. Once the water has been brought to a boil, add pasta and stir. Cook pasta until al dente, drain (reserving ¾ cup pasta water), toss with ½ tablespoon of extra virgin olive oil and set aside.
Pour 1 tablespoon of oil into a large sauté pan and place over medium-high heat. Add pancetta and sauté for 3 minutes. Drain pancetta onto paper towels and set aside.
Pour remaining oil to pan and sauté shallots for 1 minute. Add carrots, celery and garlic and continue to sauté for 2 minutes. Season with salt and pepper.
Add the squash and continue to sauté for an additional 3 to 4 minutes.
Deglaze the pan with the white wine, stir in the saffron threads and cook until the liquid has almost disappeared or until the squash has softened.
Return pancetta to the pan, with the vegetable mixture and stir in the orecchiette until well combined.
Reduce the heat to medium-low and gently fold in the herbs.
In a small bowl, whisk together the egg yolks and pasta water. Pour the mixture over the pasta and stir together. Sprinkle cheese over pasta and stir until just combined. Adjust seasonings and serve with extra Pecorino sprinkled on top.