Begin by gathering all necessary ingredients for the soup.

In a Dutch oven, add the chopped bacon and cook it over medium-high heat. Stir occasionally until the bacon is evenly browned, which should take about 5 to 10 minutes. Once cooked, transfer the bacon to paper towels to drain excess fat and retain about 1/4 cup of the rendered bacon grease in the pot.

Using the reserved bacon drippings, sauté the diced celery and chopped onion in the Dutch oven until the onion becomes soft and translucent, approximately 5 minutes. Add the minced garlic and continue to cook for an additional 1 to 2 minutes.

Next, incorporate the cubed potatoes into the mixture, tossing them to ensure they are well-coated. Sauté for 3 to 4 minutes, then return the cooked bacon to the pot. Add enough chicken stock to just cover the potatoes, cover the pot, and allow the mixture to simmer until the potatoes are tender, about 15 to 20 minutes.

Meanwhile, in a separate skillet, melt the butter over medium heat. Whisk in the flour and cook, stirring constantly for 1 to 2 minutes. Gradually add the heavy cream, tarragon, and cilantro to the skillet, whisking until combined.

Bring the cream mixture to a boil, stirring continuously until it thickens, which should take around 5 minutes. Once thickened, add this cream mixture to the potato and bacon mixture in the Dutch oven, stirring well to combine all ingredients.

To achieve a desired texture, transfer approximately half of the soup to a blender and purée until smooth. Return the puréed soup back to the Dutch oven and adjust the seasoning with salt and freshly ground black pepper as needed.

Serve the soup hot and enjoy its comforting richness!