Combine potatoes, chicken broth, cheese, onion, and jalapeño pepper in a large Dutch oven; bring to a boil. Reduce heat; simmer, uncovered, 30 minutes or until potatoes are tender. Remove from heat, and cool slightly.
Place 2 cups potato mixture in container of an electric blender; process until smooth, and set aside. Repeat procedure with remaining potato mixture. Return all pureed mixture to Dutch oven. Add butter, whipping cream, and salt; cook over low heat, stirring frequently, until butter melts and soup is thoroughly heated. Serve immediately in warm soup bowls; garnish with avocado slices, if desired.