Bring a large pot of lightly salted water to a boil. Cook orzo in the boiling water, stirring occasionally until tender yet firm to the bite, about 9 minutes. Drain well. Rinse with cold water and drain well again.

Combine orzo, cherry tomatoes, red onion, cucumber, olives, and Asiago cheese in a large bowl.

To make the vinaigrette: Whisk garlic, olive oil, red wine vinegar, lemon juice, salt, and pepper together in a small bowl; drizzle over orzo mixture and toss lightly to combine. Add basil and parsley and mix well.