Cook the pasta al dente in a pot of salted water according to package instructions. Drain the pasta, reserving 1 cup of the cooking water.
In a large skillet, heat the olive oil on MEDIUM. Add the chopped onions. Cook for 5 minutes until soft. Add the garlic and cook for one more minute until fragrant.
Add 1 1/2 cups peas to the skillet. Combine with 1 cup of pasta water. Simmer for 10 minutes, until the peas are cooked.
Transfer the sauce to an immersion blender and blend until smooth. Pass the sauce through a strain back to the skillet.
Add the cooked pasta to the skillet with the pea sauce and season with salt and black pepper. Add more pasta water if the sauce is too thick.
Add the remaining peas, and Parmesan cheese. Stir well until combined. Transfer the pasta with peas onto plates and garnish with fresh basil leaves.