1. In a medium saucepan, cover the beans with 2 inches of water. Add the garlic, thyme and bay leaf and bring to a boil. Simmer the beans over low heat, stirring occasionally, until tender, about 2 hours. Add more water as necessary to keep the beans covered by 2 inches.
2. Drain the beans and reserve the garlic and 1/3 cup of the cooking liquid. Transfer the beans, garlic, cooking liquid and 1/4 cup of the olive oil to a food processor and puree. Season with salt and pepper.
3. In a mini food processor, combine the parsley and celery leaves with the remaining 1/2 cup of olive oil and puree. Season with salt and pepper.
4. Transfer the white bean dip to a shallow bowl and make a well in the center of the dip with the back of a spoon. Pour the parsley oil into the well and serve with flatbread or pita chips.