Combine grated cucumber and onion in a small bowl. Sprinkle with salt and let stand for 10 min. Drain and squeeze dry.
Whisk yogurt until creamy smooth. Add cucumber mixture, garlic, green onions, tomato, lemon junice, minced mint or parsley, cumin and salt and pepper to taste.
Cook pasta in 4 qts boiling water until very al dente. Drain and rinse well in cold water, then drain again. Place in a large bowl and cool to room temperature, stirring occasionally to prevent pasta from sticking together.
Combine pasta with yogurt mixture. Garnish with mint or parsley springs and cucumber slices.