For potato filling, boil potato in a saucepan filled with salted water until tender, 15 to 20 minutes. Drain well and add to a mixing bowl. Mash until smooth. While still hot, add green onions, salt, black pepper, and cayenne, and mix with a spoon. Let cool for about 10 minutes while you chop the parsley and grate the cheese. Add parsley and cheese to the bowl, and mix with a spoon until thoroughly combined. Set aside until needed, or cover and refrigerate for future use.
Preheat the oven to 400 degrees F (200 degrees C).
For soda bread, add flour, salt, and baking soda to a mixing bowl and whisk for 30 seconds to combine. Make a well in the center, and pour in buttermilk. Use a fork to stir everything until you achieve a shaggy dough. Flour your hand and use it to press dough into a ball, cleaning the sides of the bowl while you do.
Generously flour a piece of parchment paper and transfer 45% of the dough on top. Press dough into a rectangle, about 1-inch thick. Flour the top generously, and place another piece of parchment paper over the top. Use your hand or a rolling pin to press and smooth dough out into a rectangle about 10 inches wide.
Peel off parchment paper, and if any dough sticks to parchment, add it to the remaining dough portion.
Spoon potato filling onto dough, pressing down lightly as you do, leaving a 1-inch border of dough uncovered around the edge.
Generously flour another piece of parchment paper; place remaining dough in the center. Press dough into a rectangle, generously flour the top, and place a second piece of parchment on top; flatten into a rectangle slightly larger than the bottom dough.
Peel parchment off the top, and turn top dough over and align to cover potato filling; remove parchment. Pinch and press top and bottom edges of dough together to seal potato filling inside. Dampen fingers with water if dough is sticking to them.
Remove any excess dough from parchment paper, and slide a baking sheet underneath. If desired, brush top of dough with a little buttermilk, to give it a more golden brown color once baked.
Bake bread in the preheated oven until nicely browned, 30 to 35 minutes. Remove from the oven and transfer immediately onto a cooling rack. Let cool to room temperature before serving.
While bread is cooling, make the optional shepherd's gravy. Melt 3 tablespoons of butter over medium-high heat in a skillet. Add lamb, onion, and salt, and cook, stirring, until everything is very well browned, 6 to 7 minutes. Season with black pepper and cayenne, and then stir in flour.
Cook and stir flour for about 2 minutes. Pour in cold chicken broth. Stir with a spatula, scraping any caramelization off the bottom of the pan. Bring gravy to a boil, stirring occasionally. Once boiling, gravy can be reduced slightly for a thicker texture, or just reduce heat to low and keep gravy hot until service.
To serve, cut bread into 1/2-inch-thick slices. Melt a little butter in a skillet over medium-high heat; add slices and cook until heated through and golden brown, a few minutes per side. Serve with the hot shepherd's gravy.
