Cook the pasta in well-salted water until just past the al dente stage. You want the pasta tender and cooked through, but not over-cooked and mushy. Remove from the heat and drain the pasta well. Transfer it back to the pot, drizzle with olive oil, and stir to coat. Set aside to cool slightly, about 15 minutes, stirring occasionally to prevent clumping.
Meanwhile, to a large mixing bowl, add the diced bell pepper, sliced cucumber, halved grape tomatoes, diced red onion, sliced pepperoncini, chopped parsley, dried oregano, and vegan feta cheese, if using. Set aside.
In a small bowl whisk together all of the vinaigrette ingredients. Alternately, you can add the ingredients to a jar with a tight lid and shake vigorously until well combined. Set aside.
Once the cooked pasta is cool to the touch add it to the bowl with the chopped vegetables. Pour the vinaigrette over everything. Toss well to combine.
Transfer to the fridge in an airtight bowl to chill until ready to serve.