To make this salad, start by bringing a large pot of well-salted water to a boil. Cook the radiatore pasta according to the package directions, until it's al dente — you want it to have a little bite to it, since it will continue to soften slightly as it sits in the dressing. Once it's done, drain it and set it aside to cool slightly.
While the pasta is cooking, prepare the dressing. Add the olive oil, pickle brine, red wine vinegar, honey, garlic powder, kosher salt, ground black pepper, and finely grated Parmigiano Reggiano to a small blender and blend until the dressing is smooth and creamy.
Next, prepare the vegetables. Slice the Persian cucumbers and radishes thinly, finely chop the snap peas, dice the red onion, and thaw the petite peas if they were frozen.
Add the cooked pasta to a very large bowl. Add the sliced cucumbers, radishes, chopped snap peas, petite peas, red onion, and crumbled feta on top of the pasta. Pour the creamy parmesan vinaigrette over everything, then toss until the pasta and vegetables are fully coated in the dressing.
Serve immediately, or cover and refrigerate until ready to eat. Store any leftovers in an airtight container in the fridge for up to three days.