Fill a large pot with water, bring to a boil, and cook the pasta in heavily salted water as per package directions or until slightly past al dente. Once cooked, drain the pasta, toss it with a little olive oil (to prevent it from sticking together) and let it cool to room temperature.
While the pasta is cooking, prepare the dressing. Whisk together the pesto, olive oil, and lemon juice in a small bowl or shake them in a jar until fully blended.
Once the pasta has cooled, transfer it to a large mixing bowl. Add the halved cherry tomatoes, thinly sliced red onion, Bocconcini, basil, parsley and dill. Gently mix to combine.
Cover with the dressing, season generously with salt and pepper, and toss gently until everything is evenly coated. Taste and adjust seasoning as needed.