Heat a large pot over medium heat and add one tablespoon of olive oil.
Once the oil is hot, sauté the onions until they become translucent, then stir in the garlic and cook for one more minute.
Add the carrots and continue sautéing for two minutes.
Pour in the chicken broth and add the orzo, cooking until the orzo is tender but still slightly firm, which takes about 10 minutes.
Meanwhile, in a separate skillet over medium heat, warm another tablespoon of olive oil.
When the oil is hot, add the shrimp, sprinkle with salt and pepper, and cook until the shrimp turn pink and are cooked through, flipping them once.
Set the shrimp aside.
Once the orzo soup is ready, stir in the lemon zest and juice, then season with salt, pepper, and dried basil.
Spoon the soup into bowls and top each serving with the cooked shrimp.