Cook orzo in salted boiling water to "al dente" according to package directions. Pour into a colander and rinse with cool water, draining the pasta well.
Pour olive oil, lemon juice, vinegar, honey, garlic, oregano, and 1/4 teaspoon kosher salt and 1/2 teaspoon black pepper into a lidded jar. Shake vigorously to combine.
Toss orzo with the cucumber, tomatoes, onion, artichoke hearts, olives, and parsley. Pour the dressing over the salad and toss to combine. Gently fold in crumbled Feta.
Season to taste with salt, pepper, and additional lemon juice, if needed (quantities will depend on the brand of Feta and artichoke hearts you've used).