Using a food processor, finely chop 2 cloves garlic and the jalapeno. Add the avocados, lime peel, lime juice and 1/2 cup cilantro leaves; season to taste with salt and pepper. Process until just combined. With the machine on, slowly pour in the chicken broth until smooth. If the soup is too thick, slowly add up to 1 cup water.
In a small nonstick skillet, toast the corn kernels over medium heat, stirring, until lightly browned. Season with salt and let cool. Stir 1 1/2 cups corn kernels into the soup.
Preheat the broiler. Rub 1 side of each toast with the remaining 2 cloves garlic and top with a slice of cheese. Broil the toasts until the cheese is softened.
Top the soup with the remaining 1/2 cup corn kernels and the remaining 1/4 cup cilantro. Serve with the toasts.