Heat the oil in a large soup pot over medium heat. Add the onions, carrots and garlic and sauté for 5 minutes, not allowing the vegetables to brown.
Add the tomatoes, and broth to the pot, turn the heat to high, and bring to a simmer. Reduce the heat to medium-low and continue to gently simmer, uncovered, for another 20 minutes.
Very carefully transfer the soup in batches to a food processor blender and puree until smooth, or use an immersion blender and puree right in the pot (or not, if you want a chunky soup). Stir in the cooked orzo and dill. Taste and adjust the seasonings.
Serve hot, with Parmesan and additional mince dill, if desired.