Add the 1 pound of quartered potatoes to a large pot and cover with water. Add 1 teaspoon of kosher salt. Bring to a boil, reduce the heat, and simmer for 30 minutes or until fork-tender. Drain and mash with a fork or potato masher. Set aside.
Make the whipped sour cream:
Combine the heavy cream, sour cream, and salt in a large bowl. Use a mixer to blend until stiff peaks form. Taste and season with more salt if desired. Transfer to the refrigerator until needed.
Make boxty batter:
Add 2 eggs to a large bowl and whisk until smooth. Add ¾ cups flour, 1 teaspoon baking powder, and 2 teaspoons salt to the bowl of eggs and whisk until combined into a thick paste.
Add buttermilk and whisk until smooth. Add mashed potatoes, grated potatoes, and grated Irish cheddar. Mix until combined into a thick batter.
Heat 1 tablespoon of neutral oil in a large skillet over medium heat. Once hot, add a spoonful of batter (about 2 to 3 tablespoons total) and smooth out into a circle. Fry for 3 to 4 minutes per side until golden brown. Transfer to a plate. Continue frying until all cakes are made, adding more oil between batches if needed. Batter yields about 8 boxty cakes total.
To serve:
Place a boxty cake on a plate and spoon the whipped sour cream on top. Finish with freshly minced chives. Enjoy!