While bringing a pot of salted water to a boil, slice the cucumber into thin half-moons and the radishes paper-thin—I like to use a mandoline for the radishes to get them as crispy as possible. Finely mince the garlic clove and set aside. Once the water boils, cook the pasta until just past al dente (about 1-2 minutes beyond the package instructions) so it holds up well when tossed with the dressing. Drain the pasta and toss immediately with 2 tablespoons of the olive oil to prevent sticking as it cools.
In a small bowl, whisk together the remaining 2 tablespoons of olive oil, apple cider vinegar, honey, minced garlic, lemon zest, salt, black pepper, and red pepper flakes. Taste and adjust the seasoning—I find the acidity needs to be bold enough to shine through once everything is mixed together. Let the dressing sit for a minute to allow the flavors to meld before using.
While the pasta cools, roughly chop the fresh dill, basil, and parsley (keeping them separate from the delicate arugula for now). Cut the mozzarella into 1/2-inch cubes. Having all your components prepped and ready will make the final assembly quick and ensure everything stays fresh and vibrant.
Once the pasta has cooled to room temperature, transfer it to a large bowl. Add the sliced cucumber and radishes from Step 1, the mozzarella cubes, and the chopped herbs (dill, basil, and parsley). Pour the dressing from Step 2 over everything and toss gently but thoroughly to coat all the ingredients evenly. Fold in the handful of arugula last—this keeps it from wilting and ensures it stays tender and peppery as a final textural contrast.