Chop the bacon into small pieces.

Melt the butter in a large saucepan over medium-high heat.

Add the chopped bacon to the saucepan and fry until golden brown and crispy.

Peel and dice the potato into small cubes.

Finely chop the onions.

Finely chop the carrot.

Finely chop the celery.

Add the diced potato, chopped onions, chopped carrots, and chopped celery to the saucepan with the bacon.

Fry the vegetables for about 10 minutes, stirring occasionally.

Pour in the chicken broth.

Season the soup with salt and pepper to taste.

Cover the saucepan and bring the soup to a simmer.

Cook for about 30 minutes, or until the vegetables are tender.

Remove the saucepan from the heat.

Pass the soup through a sieve or blend it in a food processor until smooth.

Return the blended soup to the saucepan.

In a small bowl, whisk together the cornstarch with 4 tablespoons of cold water to form a slurry.

Pour the cornstarch slurry into the hot soup and stir well.

Bring the soup to a boil, stirring constantly to prevent lumps from forming.

Reduce the heat to low and simmer for a few minutes until the soup has thickened slightly.

Thinly slice the frankfurters diagonally.

Add the sliced frankfurters to the soup and heat gently for about 5 minutes, until they are warmed through.

Taste the soup and adjust the seasoning with salt and pepper as needed.

Serve the Schwarzwald Soup hot.