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1
Preheat the oven to 300.
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2
Separate the cloves from the head(s) of garlic, peel the cloves, and place them in a single layer in a small, shallow, ovenproof baking dish.
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3
Add just enough olive oil to cover the cloves, then place in the oven and cook 45 minutes to an hour, until the cloves are very soft.
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4
Cool the garlic and oil, then transfer into a covered container or glass jar. Store in the refrigerator for up to one week.
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5
Rinse and pick through the beans, place them into a pot and cover them with 4 cups of cold tap water. Place a lid on the pot and bring it to a boil, then reduce the heat to low and cook until the beans are just tender. Season with salt and let the beans cook just a bit longer until they are seasoned. (You can do this ahead of time and store the beans in the refrigerator or freezer in their cooled cooking liquid.)
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6
In a large, heavy bottomed pot, heat the olive oil over medium heat. Add the leeks and cook for a few minutes until tender. Add the beans with their cooking liquid (you should have about 2 cups worth), the herbs, the parmesan rind, and the water or broth, cover the pot and simmer for about an hour, until the beans are tender but still a bit firm.
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7
Remove any herb stems from the soup and discard (the leaves should have fallen off into the broth). Mash the garlic to a paste and stir into the soup until it is well-incorporated, then add the potatoes and carrots. Season with salt, re-cover the pan and let it simmer another 20 minutes or so, until the potatoes and carrots are tender. Add the pasta and cook for another 10 minutes or so, until the pasta is just cooked through. Remove the parmesan rind and spoon the soup into bowls, topping with grated parmesan if desired.
