In a large heavy pot or the insert of a pressure cooker, saute the bacon until crisp. Remove the bacon to a plate lined with a paper towel to drain. Remove all but 2 tablespoons of the drippings from the pot.
Cook the onions in the bacon drippings until tender and translucent, scraping up any browned bits. Stir in the potatoes and the garlic. Cook for an additional 2 minutes, stirring.
Add the chicken stock as well as the salt, tarragon, black pepper, and cayenne.
Simmer until the potatoes are tender, about 20 minutes. If you are using the pressure cooker, fit the lid and set to pressurized. Set the machine to manual for 5 minutes. When the time is up, use the quick release to remove the lid.
Stir the soup, mashing the larger potatoes with the bowl of the ladle, until you have the texture you prefer. Stir in the cream. Adjust the seasonings and serve with the crisp bacon and other toppings.