Gather all ingredients.

Place bacon in a Dutch oven and cook over medium-high heat, turning occasionally, until evenly browned, 5 to 10 minutes. Drain bacon pieces on paper towels. Drain off all but ¼ cup of the bacon grease.

Cook celery and onion in the reserved bacon drippings until onion is soft and translucent, about 5 minutes. Stir in garlic, and continue cooking for 1 to 2 minutes.

Add cubed potatoes, and toss to coat. Sauté for 3 to 4 minutes. Return bacon to the pan, and add enough chicken stock to just cover the potatoes. Cover, and simmer until potatoes are tender, 15 to 20 minutes.

Meanwhile, melt butter in a separate skillet over medium heat. Whisk in flour. Cook, stirring constantly, 1 to 2 minutes. Whisk in heavy cream, tarragon, and cilantro.

Bring cream mixture to a boil, and cook, stirring constantly, until thickened, about 5 minutes. Add cream mixture to the potato mixture; stir to combine.

Transfer about ½ of the soup to a blender and purée. Return to the Dutch oven. Adjust seasonings to taste.

Serve hot and enjoy!