In a heavy soup pan or Dutch oven, melt the butter over medium heat.
Saute the onion and potato in the butter until the onion browns slightly and the potato starts to stick. Use a 1/4 cup of the chicken broth to deglaze the pan, loosening any browned potato from the bottom of the pan.
Add the sliced lettuce, stir, and cover to steam briefly. Stir every minute or so and continue until the lettuce has thoroughly wilted.
Add the chicken broth and simmer for about 5 minutes.
Turn off the heat, add the fresh basil and process with an immersion blender. Adjust the taste with salt and pepper.
Add the ham and cheese and stir very briefly. Try not to stir so much that the cheese disappears.