Place the bacon in a medium pot set over medium heat. Cook until slightly crispy, and then stir in the leek, carrot and garlic and cook 3 to 4 minutes. Mix in the flour and cook 2 minutes more. Slowly, stirring constantly, pour in the stock. Mix in the potatoes and tarragon, return to a simmer, and simmer until the potatoes are just tender, about 10 minutes. Mix in the cream and green onions and heat through 2 minutes. Season with salt and pepper and serve.