In a large stockpot, cook the spaghetti in plenty of boiling salted water for about 10 minutes; it should still be a little firm.
At the same time, heat a 2-count drizzle of olive oil in a large skillet over medium-low heat. Add the pancetta, and stir it around. When the fat starts to render, after about 3 minutes, add the onion and bay leaf. Cook and stir until the onion caramelizes, about 10 minutes. Now add the peas and cook for 2 minutes just to heat them through.
Drain the pasta, reserving 1 cup of the starchy water for the sauce. Fold the goat cheese into the hot pasta and give it a toss so it melts. Scrape the pancetta, onions, and peas into the pasta pot (toss the bay leaf). Add the Parmigiano, parsley, and lemon juice. Slowly pour in the reserved pasta water to dissolve the cheese and thin it out to a sauce consistency. Hit it with a healthy dose of olive oil and quite a few turns of freshly ground black pepper to give it bite. Return the noodles to the pot and gently toss to coat in the sauce. Split the pasta between 2 large bowls and shower it with the shredded basil.
Edited: October 14th, 2009