Begin by melting a tablespoon of butter and olive oil in a large pot or Dutch oven over medium heat until the butter is liquid.
Add the chopped onion, celery, and carrots to the pot. Stir occasionally and cook until they become soft, which usually takes 4 to 6 minutes.
Introduce the chopped parsley and stir briefly for about 10 seconds until it becomes fragrant.
Incorporate the chopped and peeled potatoes into the mixture.
Pour 2 cups of water and 4 cups of chicken broth into the pot. Increase the heat until it starts simmering actively.
Reduce the heat to maintain a gentle simmer and cook until the potatoes turn very soft approximately 15 minutes.
Carefully use an immersion blender or blend it in batches using a regular blender to achieve a smooth consistency.
In a separate saucepan, melt the remaining 2 tablespoons of butter to create a roux.
Add 2 tablespoons of all-purpose flour to the melted butter. Cook over low heat while whisking continuously until the flour loses its raw smell, which should take about 5 minutes.
Warm 1 cup of half and half in the microwave until it's hot, avoiding boiling. Gradually incorporate a portion of the hot half and half into the hot roux while whisking continuously until the mixture is smooth.
Combine the roux mixture with the remaining hot half and half, stirring to ensure even consistency.
Gently stir this mixture into the simmering potato soup.
Add the crumbled bacon bits and season the soup with 1/2 teaspoon of salt and freshly ground black pepper to your taste.
Allow the soup to simmer for an additional 10 to 20 minutes to enable the flour to soften and absorb the liquid. Adequate simmering is essential to avoid graininess in the roux.
Once the soup is thoroughly heated and well-blended, it's ready to be served hot. Optionally, garnish it with chopped parsley or shredded cheese.
Savour your homemade Eat N Park Potato Soup!