Place the celeriac cubes in a medium saucepan and add the vegetable broth. Bring to a boil over medium-high heat, then reduce to a steady simmer. Cover partially and cook for 20 to 25 minutes, or until the celeriac is very tender when pierced with a knife.
While the celeriac cooks, make the garlic oil. Add the sliced garlic and 45 ml olive oil to a small skillet or saucepan over low heat. Cook gently for 5 to 7 minutes, stirring occasionally, until the garlic is lightly golden and fragrant. Do not let it brown deeply. Remove from the heat and set aside.
When the celeriac is tender, use a slotted spoon to transfer it to a blender or food processor. Add the white beans, 30 ml extra-virgin olive oil, salt, black pepper, and lemon juice.
Add 120 ml of the cooking broth to the blender and puree until smooth. Stop and scrape down the sides as needed. If the mixture is too thick, add more cooking broth, 15 to 30 ml at a time, until the puree reaches your preferred consistency.
Taste the puree and adjust with more salt, black pepper, or lemon juice if needed. Blend once more briefly to combine.
Spoon the warm puree onto a serving plate or into a shallow bowl. Swirl the top with the back of a spoon, then drizzle over the garlic oil and scatter with chopped parsley. Serve warm.