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1
Drain the white beans and combine with 2 quarts water in a large, heavy soup pot or Dutch oven.
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2
Bring to a boil.
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3
Skim off any foam, then add half the onion, half the garlic and the bouquet garni.
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4
Reduce the heat, cover and simmer 45 minutes.
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5
Add salt to taste.
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6
Heat the olive oil in a heavy skillet, and add the remaining chopped onion and a generous pinch of salt.
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7
Cook, stirring, until tender, about five minutes.
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8
Add the leeks and remaining garlic.
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9
Stir together for a few minutes, and add the tomatoes.
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10
Cook, stirring, until the tomatoes have cooked down slightly and the mixture is fragrant, five to 10 minutes.
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11
Stir this mixture into the soup pot, add all of the remaining vegetables except the green beans, and bring back to a simmer.
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12
Cover and simmer over low heat for 45 minutes to an hour.
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13
Taste and adjust the seasonings.
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14
While the soup is simmering, blanch the green beans for five minutes in salted boiling water.
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15
Transfer to a bowl of ice-cold water.
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16
Drain and set aside.
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17
To make the pistou, mash the garlic with a generous pinch of salt in a mortar and pestle.
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18
Remove it and set aside.
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19
Grind the basil to a paste in the mortar, a handful at a time, then add the garlic back in and mix together well.
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20
Work in the olive oil a tablespoon at a time, then stir in the cheese.
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21
Add the pasta to the simmering soup about 10 minutes before serving, and cook until cooked al dente.
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22
Add pepper, taste and adjust salt.
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23
Stir the blanched green beans into the soup and heat through.
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24
Serve, adding a spoonful of pesto to each bowl for guests to stir in.
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25
Pass additional Parmesan for sprinkling.
