In a medium saucepan cook the leeks, potato, and garlic for 10 minutes in boiling water or until potatoes are tender; drain well.
In a food processor or blender combine the leek mixture, thawed corn, cream cheese, and 3/4 of chicken broth. Cover and process or blend until smooth; set aside.
In the same saucepan melt butter. Stir in flour, salt, and pepper. Add milk all at once. Cook and stir until slightly thickened and bubbly. Cook and stir 1 minute more.
Stir in remaining corn, parsley, remaining 3/4 broth, and blended vegetable mixture. Cook and stir until heated through. If necessary, stir in additional milk to reach desired consistency. Season to taste with salt and pepper.