In a medium pot, add 2 cups of water and the chicken and bring to a boil over high heat. Reduce the heat to medium-low and simmer for 15-20 minutes. Remove from the heat.
While the chicken is simmering, heat the olive oil in a large pot over medium-high heat. Add the shallots, garlic and sunchokes, and cook for 5-6 minutes, stirring. Add the rosemary and cook for an additional minute, stirring occasionally. Add the milk and cook over low heat for 15 minutes. Remove from the heat. Carefully puree the mixture and 1/2 cup of water in a food processor or blender for approximately 2 minutes or until smooth. Return the puree to the pot.
Add the vegetable stock, lemon juice, chicken and season with salt and pepper and bring to a boil. Lower the heat and gently simmer for 30 minutes, stirring occasionally.
Divide the soup into individual bowls. Sprinkle the fresh parsley over the top. Serve immediately.