Prepare your grill for direct heat cooking with medium high heat. When ready, grill the corn and potatoes, covered, for 20 minutes or until tender, turning once during cooking.
Spray the zucchini slices with cooking spray, grill uncovered for about 4-5 minutes or until tender, turning once during cooking.
Cut the corn kernels off the ear, cut the potato into cubes, and cut the zucchini into bite size pieces.
Melt butter in a large saucepan on medium heat, when hot, add the onion and saute for about 5 minutes or until tender.
Stir in the flour, thyme, and white pepper, cook while stirring for 1 minute.
Stir in the beer and milk, and bring to a boil then reduce heat to medium low. Simmer for 1 minute.
Stir in the corn, potato, zucchini, and cheese. Simmer until heated through.
Ladle into bowls, serve and enjoy.