Melt the unsalted butter in a large stock pot over medium- high heat. As the butter begins to sizzle, add the cleaned, cut ramps.
Season the ramps with salt and pepper. Saute until the ramps begin to wilt and turn soft, which should take about six minutes.
Add the bay leaf and the chopped garlic and stir for about two minutes.
Add the stock and the potatoes. Bring the mixture to a boil. Reduce the heat to medium and simmer the soup uncovered. Continue cooking until the potatoes are fork tender and the mixture is thick and creamy. This should take about one hour.
Remove the soup from the heat, discard the bay leaf. Add the cream to the mixture very slowly, stirring constantly. Check for seasoning and add more salt and pepper if desired.
Brush both sides of each piece of bread with truffle oil. Place a slice of cheese on top of each of the four pieces of bread. Place the remaining slices of bread on top of the cheese.
Fry these sandwiches for 2 to 3 minutes each on a hot griddle, or until the cheese is melted and the bread is a beautiful golden color.
Cut each sandwich into five finger sized slices and serve with the piping hot soup.