Heat oil in a large skillet over medium heat. Cook and stir zucchini and garlic in the hot skillet until lightly browned. Remove from heat and set aside.
Purée tomatoes, onion, and chile pepper in a blender or food processor, leaving a few small chunks.
Mix together tomato purée and vegetable broth in a large pot. Season with tarragon, dill, salt, and pepper. Bring to a boil, reduce heat to low, and stir in zucchini-garlic mixture. Cover and cook for 45 minutes.