Cook the pasta in heavily salted water 1 or 2 minutes less than the package instructions until just al dente. Drain well and put the pasta into a large serving bowl.
While the pasta is cooking combine 1 cup of the basil with the garlic, finely grated lemon zest, lemon juice, salt and pepper in a blender and blend until the basil is finely minced and the mixture is combined. Take the plastic insert from the top of the blender out and slowly stream in the olive oil with the machine running. You want a thick dressing but not as thick as mayonnaise. If the mixture is too thick, add more olive oil.
Once the pasta is cooked and drained pour the dressing over the warm pasta. Toss well and let cool.
Roll the remaining basil leaves up like a cigar and cut into thin slices with a sharp knife. When the pasta has cooled, add the basil, tomatoes and bocconcini. Cover and refrigerate for at least half an hour or up to two days. Taste and adjust seasoning with more salt and pepper if needed.