In an extra-large bowl, place the romaine and arugula. In a small bowl or measuring cup, make the dressing: Whisk together the olive oil, vinegar, mustard, garlic, salt, and pepper until smoothly combined (or put all of the dressing ingredients in a mason jar, seal, and shake to combine). Pour half of the dressing over the salad and toss to coat. The leaves should be lightly moistened.
Arrange the salami, prosciutto, artichokes, olives, red peppers, and tomatoes on top of the greens. Drizzle with a bit more dressing to moisten. Sprinkle with feta and parsley. Enjoy immediately or refrigerate for 1 hour prior to serving.