Preheat your oven to 400°F (200°C).
In a bowl, combine the trimmed artichoke quarters with 1 tablespoon of olive oil, dried oregano, salt, and pepper. Toss the artichokes until they are evenly coated with the seasonings.
Place the seasoned artichokes on a baking sheet in a single layer. Roast them in the preheated oven for about 25 minutes or until they turn golden brown and are tender when pierced with a fork.
While the artichokes are roasting, prepare the olive mixture. In a separate bowl, combine the green and Kalamata olives, lemon zest, lemon juice, and the remaining tablespoon of olive oil. Toss the mixture gently to marry the flavors.
Once the artichokes are roasted to perfection, remove them from the oven and let them cool slightly.
In a large serving bowl, assemble the salad. Start with a bed of fresh arugula, followed by the roasted artichokes, cherry tomatoes, red onion slices, and the olive mixture.
Top the salad with crumbled feta cheese for an extra burst of flavor.