While the vegetables are simmering for the green tomato oil, prepare the white bean puree.
Heat 2 teaspoons extra virgin olive oil in a large pot over medium heat. Once hot, add the shallots and celery and cook for 7-8 minutes until softened and beginning to brown.
Add the roasted garlic and cook for 1 minute until fragrant.
Add the chicken stock and bring to a boil. Add the potatoes and both cans of beans. Season with salt, Old Bay, and white pepper. Reduce heat, cover and simmer for 20-25 minutes or until the potatoes are fork tender. Note: Stir the beans occasionally and add more liquid as necessary to prevent them from sticking.
Pour in the heavy cream and simmer for 10-15 minutes longer until thickened. Add 2-3 tablespoons of the reserved cooking water from the green tomato oil. Taste and season again with salt and pepper.
Using an immersion blender, blend the white beans until smooth and creamy. Keep warm.