Start the Tzatziki sauce: Grate the cucumber on a box grater and spread in a single layer on a paper towel-lined baking sheet. Sprinkle with 1 teaspoon salt and let stand for 30 minutes to allow the liquid to release.
Meanwhile, bring a medium saucepan of salted water to a boil. Add the orzo and cook 9 to 10 minutes or until al dente. Drain the orzo and rinse under cold water to cool. Set aside.
Finish the Tzatziki sauce: Gather the grated cucumber in the paper towels and squeeze thoroughly to remove the liquid. Transfer the cucumber to a medium bowl. Stir in the yogurt, lemon juice, garlic, dill, parsley, and olive oil. Season to taste with salt and pepper. Refrigerate until ready to serve.
Make the Greek vinaigrette: Whisk together the vinegar, honey, and oregano in a small bowl. Gradually add the olive oil and whisk until emulsified. Season with salt and pepper to taste.
Assemble the bowls: Divide the hummus between serving bowls. Top evenly with the chickpeas. Divide the orzo between the bowls. Top with mixed greens, tomatoes, cucumbers, olives, and feta. Drizzle with desired amount of vinaigrette.