Preheat the oven to 400°F. Line a baking sheet with parchment, then add the slices of bacon in a single layer.
Bake in the oven until crispy, about 15-20 minutes. Remove from the oven and transfer to a paper-towel lined plate. Once cool, crumble or roughly chop.
Meanwhile, bring a large pot of salted water to a boil. Add the pasta, and cook according to package instructions, or until al dente. Drain and rinse with cold water to stop the cooking. Add to a large bowl and toss with a small drizzle of olive oil to prevent sticking.
Make the Dressing: Add the mayonnaise, olive oil, lemon juice, salt, black pepper, and sugar to a bowl. Thoroughly whisk together and keep in the fridge until ready to use.
Assemble: Add the peas, bacon, chives, grated parmesan, and shaved parmesan to the large bowl of pasta.
Pour the dressing over the salad and mix well to combine. Serve immediately, or keep chilled in the fridge until ready to serve!