Slice the fennel bulbs thinly; chop the fennel fronds and set them aside to use later.
In a large heavy sauce pot over medium temperature, heat the olive oil; add the sliced fennel bulb, thyme, and butter.
Saute, stirring occasionally, until fennel is golden brown and caramelized, about 15 to 20 minutes.
Add the white wine, garlic, stock, and small white beans and simmer gently for 30 minutes.
(At this point, if you'd like a creamy soup you can take out half of the soup and puree it in a blender, then add it back into the pot.).
Season soup to taste with sea salt and white pepper.
Garnish with a little drizzle of extra virgin olive oil and a bit of chopped fennel frond, and serve.
Note: more beans can be added to the soup, if you like (a couple of cups worth), or you can use other kinds of beans or a combination. And yes, the amounts are correct in the recipe - it's a gallon of stock. This makes a lotta soup!