Bring a large pot of salted water to a boil. Add the orzo and cook according to the package instructions (about 8 minutes) until al dente.
Drain the orzo, rinse under cold water to stop the cooking process, and let it cool completely.
In a small bowl, whisk together olive oil, lemon juice, red wine vinegar, Dijon mustard, minced garlic, dried oregano, salt, and black pepper. Set aside.
In a large mixing bowl, combine the cooled orzo, cherry tomatoes, cucumber, red bell pepper, red onion, artichoke hearts, vegan feta, chickpeas and chopped basil.
Pour the dressing over the salad and toss well to combine. Taste and add more salt if needed, depending on the saltiness of the feta cheese used.
Let the salad sit for at least 15 minutes before serving to allow the flavors to meld. Serve cold or at room temperature.
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Notes
Store leftover orzo salad in an airtight container in the fridge for up to 3 days. Be sure to mix well before serving again since the dressing will settle.