While the pasta is cooking, prepare the sauce.
Pour the hot pasta water over the broccoli in a bowl and let sit for 2 minutes (this will blanch the broccoli), then drain.
Place the mayo, lemon juice, and basil into a jar and use an immersion blender to blend (or use a food processor) and blend until smooth, add salt and pepper to taste.
Once pasta is cooked, drain then cover with cold water to chill pasta.
When the pasta is cold, drain well.
Stir pasta with dressing. and add the broccoli and mix well.
Chill until cold.
Serve with additional lemon if desired.