Peel the prawns and reserve the shells. Cut each prawn, lengthwise, in half; store in the fridge until needed. Melt 1/2 Tbsp. of the butter in a pot set over medium heat. Add the prawn shells and cook until bright red, about 3–4 minutes. Pour in the stock and wine, bring to a gentle simmer, and simmer 20 minutes. Strain the prawn-flavoured stock.
Melt the remaining butter in a second pot set over medium heat. Add the onion, celery and garlic and cook 3–4 minutes. Mix in the flour and cook 2 minutes more. Slowly, stirring constantly, pour in the prawn-flavoured stock. Mix in the tarragon, cream and potatoes, return to a simmer, and simmer until the potatoes are just tender, about 10 minutes. Mix in the corn and reserved prawns, return to a simmer, and simmer until the prawns are cooked through, about 5 minutes. Season with salt and pepper and serve.