Bring a large pot of generously salted water to a boil. Add the pasta and cook according to package instructions. Drain the pasta and toss with the olive oil.
While the pasta is cooking, in a small bowl, whisk together the egg yolks, Parmesan cheese, heavy cream and lemon zest.
Heat a large saute pan over medium heat. Add the bacon pieces and cook until the bacon is crisp and cooked through. Use a slotted spoon and remove the bacon, keeping as much of the bacon drippings in the pan as possible.
Return the pan (with the bacon drippings) to medium heat. Add the onions and saute until the onions are softened, about 2 minutes. Add the minced garlic and saute an additional 30 seconds until fragrant.
Turn the heat to medium-high and whisk in the egg/cream mixture. Let the sauce bubble briefly and then quickly add in the pasta, peas and the cooked bacon (you don't want too much of the egg/cream mixture to evaporate, so work quickly).
Toss so that the ingredients are well mixed throughout. When the pasta is heated through (about 4 minutes) season with salt and pepper to taste (go easy on the salt - remember the bacon is salty and you've salted the pasta water.) Toss well with the torn basil leaves and add additional Parmesan cheese, if desired.