For the Garlic: Preheat the oven to 400 degrees. Cut the top off of a head of garlic, so the top of each garlic clove is visible. Drizzle on a little olive oil (~½-1 teaspoon), and rub in with your fingers. Wrap in foil and bake for 50 minutes-1 hour, until golden.
Heat the olive oil in a large soup pot or dutch oven over medium heat. Add the leeks and a small pinch of salt, and cook, stirring frequently, until softened (about 3 minutes). Stir in the carrots, celery, and sage, and cook for 5-7 minutes, until the vegetables are tender.
Pour in 2 cups of the broth (reserving ½ cup for later), along with the milk, pepper, and beans. Boil over medium heat, uncovered until soup is thickened, about 30-40 minutes. If your soup takes longer than 50 minutes and you’re running low on liquid, add a little water (¼ cup at a time) as needed.
Once the beans are tender, transfer one cup of the soup to a blender along with the remaining 1/2 cup of broth and 4-6 cloves of roasted garlic, and blend until smooth. Stir the blended soup back into the pot. Taste and add salt as needed to taste.