Melt the butter in a large pot over medium heat. Add the onion and garlic, and cook until softened and fragrant. Add the flour and stir to form a paste. Cook 2-3 minutes, or until golden.

Slowly add the chicken stock and milk, whisking constantly to prevent lumps. Add the red potatoes and carrots, and bring to a simmer. Simmer 15 minutes, or until the potatoes have softened and are nearly cooked.

Add the sweet corn and zucchini, and continue to simmer for 5-10 minutes, stirring occasionally. When the soup has thickened and the vegetables are tender, remove from heat and stir in the cheese, salt, and pepper. Taste and adjust seasonings as needed.