Put 5L of water and the 2 tsp of salt in a pot, then bring to a boil. Then get a large bowl of cold water and fill it with your ice.
Whisk the crème Fraiche, egg, egg yolks, parmesan cheese and a generous pinch of black cracked pepper in a large bowl until well combined. Set aside.
Put the broccolini in your salted boiling water, boil for 2 minutes, then use a pair of tongs to transfer it to the ice-cold water (do not discard the boiling water). After about 20-30 seconds, strain the broccolini and set aside.
Add the pasta to the pot of water and boil for 8-9 minutes. Before you drain the pasta, get a large cup and scoop out some of the pasta water, you'll need that water later. Drain the pasta and set aside.
Pre-heat a large pan over medium heat, add some olive oil and then add your garlic. Fry the garlic for about 30-40 seconds and then add your broccolini. Toss the broccolini and the garlic together, then add your pasta.
As soon as everything is well combined, put the pasta on a platter and serve.