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.
Substitutions for Tomato Orzo Soup
You could also use rice or any cooked grain instead of the orzo, and basil or oregano instead of the dill. You could add some chopped fennel and/or some chopped celery when you add the carrots (I love both of these additions, but in the interest of keeping the recipe as easy and streamlined as possible, I am just mentioning them as optional). If you use fennel, and have some fresh fronds from the top, those can be minced for a lovely finishing garnish as well.