Wrap the grated potatoes in a clean tea towel or several thicknesses of cheesecloth. Working over a medium bowl, tightly twist the ends of the rowel in opposite directions, to squeeze out as much liquid as possible. Set the bowl of potato water aside for 10 minutes.
Put the grated potato into a large bowl, add the mashed potatoes, and mix well to combine thoroughly.
Carefully pour off and discard the liquid from the bowl with the potato water, leaving a layer of thick white potato starch at the bottom. Add the starch to the potato mixture, then add the flour and baking soda and season to taste with salt. Transfer the mixture to a lightly floured surface and knead for 1 or 2 minutes or until a thick dough forms.
On a lightly floured surface, press the dough with your hands into a disk, then roll it out into a circle about ¾ in/2 cm thick. Using a cookie cutter or the floured rim of a drinking glass, cut the dough into 3-in/7.5-cm rounds.
Melt the bacon fat or butter in a large skillet over medium heat. Add the boxty in a single layer and fry for 3 to 4 minutes per side or until golden brown.
There are two other common ways of cooking boxty:
1. Cut the dough into cakes as described and then drop them into a large pot of gently boiling salted water and cook for about 40 minutes. (Be sure to use very starchy potatoes if you’re going to make boiled boxty, or they’ll fall apart in the water.) Carefully drain and cool to room temperature, then halve crosswise and fry as above. (Boiled boxty cakes are sometimes called “hurlcys.”)
2. Shape the dough into a circle about ¾ in/2 cm thick and cut into wedge-shaped furls (quarters). Put onto a lightly greased baking sheet and bake in a preheated 300°P/150°C (Gas Mark 2) oven for 45 to 50 minutes, or until done, turning them halfway through.