1 To make the soup: Put the onion and oil in a large sauce pan over medium-low heat and cook, stirring occasionally, until the onion is tender but not browned, about 5 minutes. Add the carrots, garlic, and rosemary and stir well. Cover and cook until the carrots begin to soften, about 5 minutes.
2 Add the broth and garbanzo beans and bring to a boil over high heat. Reduce the heat to low and cover with the lid ajar. Simmer until the carrots are very tender, about 30 minutes. Discard the rosemary sprig. Using an immersion blender, puree the soup in the saucepan until it is smooth. (Or let the soup cool, puree in batches in a blender with the lid ajar, and reheat before serving.) Season to taste with the salt and pepper.
3 To make the garbanzo “salad”: Whisk the lemon juice, oil, and chopped rosemary in a medium bowl. Add the garbanzo beans and toss to combine. Season to taste with the salt and pepper. Set the mixture aside at room temperature.
4 To make the fried rosemary: Put the oil and rosemary in a small skillet over medium heat and cook, occasionally turning the sprigs, just until the rosemary leaves are crisp, about 3 minutes. Transfer the sprigs to paper towels to drain and cool and discard the oil. Remove the leaves from the stems and discard the stems.
5 To serve, spoon the soup into bowls. Add a spoonful of the room-temperature garbanzo “salad” into the center of each serving and sprinkle with the fried rosemary.