Bring a large pot of water to a boil.

Stack up the bacon and chop into 1/2 inch slices. Toss in a skillet over medium heat. Saute until crispy.

Add the pasta to the water and boil until el dente according to the package directions about 6-8 minutes usually.

Meanwhile, wash the radicchio and shake dry. Stack up the leaves and slice thinly into strips.

Toss the minced garlic in with the bacon and after about 30 seconds add the radicchio. Saute until wilted. Finish with the tablespoon of butter or olive oil, if desired.

While whisking the eggs madly, add the black pepper, grated parmesan and 1/4 cup of the pasta water. Whisk until the hot water is incorporated otherwise it could scramble your eggs. Undesired.

Drain the pasta well and toss with the radicchio over medium heat until fully intertwined. Take the pan off of the heat. While moving the pan and tossing the pasta drizzle on the beaten eggs. The sauce will cook on to the pasta and radicchio.

Please NOTE:
Since the egg sauce is essentially cooked onto the pasta, the eggs are relatively uncooked. If you are concerned you can continue to cook the pasta over the heat when you drizzle on the sauce. It will be less attractive, but the eggs will be a bit safer.