Whisk the vinegar, mustard, salt, and pepper to taste in a small bowl. Gradually whisk in the oil to make a smooth dressing. Set aside.
Bring a large pot of salted water (about 1 tablespoon kosher salt to 4 quarts water) to a boil. Add the pasta and cook until al dente; drain, then pour pasta into a large bowl. While the pasta is still warm, pour a couple tablespoons of the dressing over the pasta and toss so that the pasta doesn’t stick together as it cools. Let it cool to room temperature, tossing now and again to help the cooling process and to prevent sticking.
When the pasta has cooled, add the sun-dried tomatoes, artichokes, basil, onion, olives, saute spice, and oregano and toss. Add the vinaigrette and toss again until the pasta ingredients are evenly coated. Add the cheeses and lightly toss. Chill until ready to serve.