In a large heavy-bottomed pot, place 1 Tb of salt and potatoes in 1/4 -1/2 gallon of water (or just enough to cover the potatoes. Bring to a boil over high heat.
Allow to simmer for 10-15 minutes until tender. Drain water and allow potatoes to sit in a strainer for 5 minutes to allow all water to drain.
Place potatoes, Dijon mustard, horseradish, 2 Tb of butter, heavy cream, remaining 1 Tb of salt, pepper and chives (or green part of scallions or leek) back into the same pot you used to boil the potatoes.
With a large kitchen spoon, stir and smash potatoes until mashed but still chunky, Adjust seasoning of salt and pepper to taste.
Using an ice cream scoop, portion a 3-ounce scoop onto a baking sheet oiled with olive oil. Form potatoes into a cake shape and top with remaining 1 Tb of butter, dividing equally among 10 potato cakes.
Place potatoes under the broiler (or in a toaster oven on broil) for 4-5 minutes until golden brown.