Heat olive oil in a medium pot over medium heat.
Add the sausage, breaking it up into small pieces. Let it brown and develop some color before stirring too much. Continue cooking until nicely browned, about 8 to 10 minutes. Remove from the pan and set aside on a paper towel-lined plate.
In the same pot, add the shallot with a pinch of salt and cook until softened, about 2 to 3 minutes.
Pour in the white wine and let it cook down until mostly evaporated, about 2 minutes.
Add the pastina, followed by 3 cups of chicken broth, and bring to a simmer. Cook, stirring often, until the pastina is tender, adding up to ½ cup more broth as needed.
When the pastina is just about done, stir in the grated garlic.
Turn the heat off and let it sit for about 1 minute so it’s no longer bubbling.
Stir in the grated cheese first, then add the egg yolks, stirring constantly until glossy and creamy.
If it feels too thick, add a splash of broth or water to loosen.
Stir the sausage back in, then finish with butter (if using), lemon zest, lemon juice, and plenty of black pepper.
Taste and adjust with more lemon, salt, or cheese as needed.
Serve right away with parsley, extra Parmesan, a drizzle of olive oil, and black pepper on top.
