Potato and Broccoli Soup

If you're like me, you hate to waste all those broccoli stems, which makes up most of your bunch of broccoli. This recipe makes use of them, as well as the florets.

2 tablespoons butter
1 onion, chopped
2 cloves garlic, minced
1 3/4 pounds broccoli, thick stems peeled and diced (about 2 cups), tops cut into small florets (about 1 quart)
1 1/2 pounds boiling potatoes (about 5), peeled and cut into 1/2-inch cubes
3 cups canned low-sodium chicken broth or homemade stock
3 cups water
1 3/4 teaspoons salt
1/4 teaspoon fresh-ground black pepper
1/2 cup grated Parmesan cheese
DIRECTIONS
In a large pot, melt the butter over moderately low heat. Add the onion; cook, stirring occasionally, until translucent, about 5 minutes.
Add the garlic, broccoli stems, potatoes, broth, water, salt, and pepper. Bring to a boil. Reduce the heat and simmer until the vegetables are almost tender, about 10 minutes.
In a food processor or blender, pulse the soup to a coarse puree. Return the soup to the pot and bring to a simmer. Add the broccoli florets and simmer until they are tender, about 5 minutes. Stir 1/4 cup of the grated Parmesan into the soup, and serve the soup topped with the remaining cheese.
VARIATION:
 If you'd prefer a completely smooth soup, add the broccoli florets to the pot after the potatoes have cooked for five minutes, and continue simmering until all of the vegetables are tender, about five minutes more. Puree the soup until smooth. Serves 6.