Prepare an ice bath and set it near the stove. Bring a large pot of salted water to a boil, then add the asparagus. Cook until the asparagus is crisp-tender and bright green, about 2 to 3 minutes (green beans may need a minute longer). With a slotted spoon, transfer the asparagus to the ice bath to stop its cooking (do not drain the boiling liquid). Let the asparagus cool for 2 to 3 minutes, then with the slotted spoon, transfer it to towels and pat dry.
Return the water to a boil and add the pasta. Cook until al dente according to package instructions. Drain into a colander, then rinse with cool water to stop the cooking. Shake the colander several times, then set the colander on towels or a plate and allow the water to continue to drain. You can also set it in the sink to drain (just don't forget about it and accidentally add soap).
In a VERY large bowl, place the onion. Add the 2 tablespoons of the vinegar. Add the asparagus, bell pepper, artichokes, tomatoes, mozzarella pearls, and chicken (no need to stir again just yet).
In a small bowl or liquid measuring cup with a spout, briskly whisk together the oil, mustard, garlic, oregano, black pepper, red pepper flakes, ¾ teaspoon salt, and the remaining 2 tablespoons vinegar until the ingredients all come together into a smooth dressing.
Shake the pasta in the colander once more to remove any last water, then add it to the bowl with the vegetable mixture.
Pour in about 2/3 of the dressing, then stir to coat.
Stir in the basil.
Taste, add additional dressing, and season with additional salt, pepper, or red pepper flakes as desired. Serve immediately, or refrigerate until ready to serve.
Notes
TO STORE: Refrigerate leftover pasta salad in an airtight storage container for up to 4 days.