John's favorite pasta is carbonara!
Bring a large pot of water to a boil for the pasta.
In a small saucepan, warm the stock and saffron over low heat and keep at a low simmer.
In a large skillet, heat 3 tbsp. oil, three turns of the pan, over medium. Add the pancetta and cook, stirring occasionally, until the fat renders, about 5 minutes.
In a medium bowl, whisk up the egg yolks and cheese.
Salt the boiling water and add the pasta. Cook until 1 minute shy of the package directions.
In a second large skillet, heat the remaining 1 tbsp. oil, one turn of the pan, over medium-high to high. Add the shrimp and cook, stirring often, until pink, about 1 minute; season with salt. Add the garlic and crushed red pepper and toss for a minute more. Add the vermouth, shaking the pan to combine. Add the butter and let it melt into the sauce. Remove from heat. Stir in the lemon juice.
Gradually whisk the warm saffron stock into the egg yolks to gradually cook the yolks without scrambling them. Drain the pasta. Add the pasta to the skillet with the pancetta and toss to coat well. Add the egg mixture and toss vigorously until the sauce thickens and absorbs into the pasta, about 1 minute. Toss in the shrimp mixture and the parsley. Serve immediately.