In a Dutch oven, cook the bacon over medium heat until done.
Remove bacon from pan, and set aside.
Drain off all but 1/4 cup of the bacon grease.

Cook celery and onion in reserved bacon drippings until onion is 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.

In a separate pan, melt butter over medium heat.
Whisk in flour.
Cook, stirring constantly, for 1 to 2 minutes.
Whisk in the heavy cream, tarragon, and cilantro.
Bring the cream mixture to a boil, and cook, stirring constantly, until thickened.
Stir the cream mixture into the potato mixture.

Puree about 1/2 the soup, and return to the pan.

Adjust seasonings to taste.