Bring a large pot of well-salted water to boil. Cook pasta to one minute shy of package instructions for 'al dente' and taste for your desired doneness, cooking a minute longer if desired.
While the water comes to a boil/the pasta cooks, ready everything you need for the sauce. Weigh (or measure) out the goat cheese and crumble it into a very large bowl. Sprinkle the pepper, salt, and red pepper flakes over the goat cheese crumbles. In a small bowl, whisk together the olive oil and lemon juice. Wash and dry the baby arugula, slice the cherry tomatoes into rounds (and tomato knife makes a big difference here), and pit then slice the Kalamata olives, setting the prepared vegetables aside in a separate bowl.
Just before the pasta is done, scoop out a cup of the hot cooking water and set it aside. Drain the pasta quickly into a colander, then immediately drop the piping hot pasta into the large bowl containing the crumbled goat cheese. Toss to combine. The goat cheese will be too thick to coat the noodles properly; now pour ⅓ cup of the hot pasta cooking water plus the olive oil and lemon juice into the bowl to help loosen the sauce, and continue tossing, tossing, tossing, adding another ⅓ cup of pasta water if necessary, until you've formed a creamy sauce that coats the pasta evenly.
Add the arugula, sliced cherry tomatoes, and sliced olives, toss multiple times to distribute. Taste and adjust as necessary with more olive oil for richness, salt/pepper/red pepper flakes to make the flavors "pop", or lemon juice for acid zing, or pasta water for a wetter sauce.
Serve immediately. This salad is great at slightly above room temperature (which it will be at this point) but it's also quite good chilled. It will keep in an airtight container in the refrigerator for 2-3 days.