Let’s break down the process into easy-to-follow steps.

Step 1: Simmer Corned Beef. Put the corned beef in a pot with the thickly sliced onion and celery. Sprinkle the contents of the spice packet over the top. Pour in enough cold water to cover the ingredients. Turn the heat to high and bring to a boil. Skim off and discard any foam that rises to the surface, if desired.

Step 2: Cover and Cook. Once boiling, reduce the heat to low, cover the pot, and simmer until the meat is almost fork-tender, about 3 ½ hours. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C).

Step 3: Cool Beef, Prepare Broth. Carefully remove the corned beef to a bowl and let it cool. Taste the broth and add salt if needed.

Step 4: Cook Cabbage. Bring the broth to a boil over high heat. Add the cabbage to the boiling broth. Cook until the cabbage just starts to soften and sweeten up, about 5 minutes. Use a slotted spoon to remove the cabbage to a bowl.

Step 5: Cook Carrots. Add the carrots to the boiling broth. Cook until the carrots start to soften, about 5 minutes. Use a slotted spoon to remove the carrots to a bowl.

Step 6: Cook Potatoes. Add the potatoes to the boiling broth and reduce the heat to medium. Cook until tender, 15 to 20 minutes.

Step 7: Slice Corned Beef. While the potatoes are cooking, slice the cooled corned beef along the fatty seam to separate it into 2 pieces. Identify the direction of the meat fibers and cut across them (against the grain) to slice the beef into ¼-inch thick slices, trimming off and discarding any giant pieces of fat. Set aside.

Step 8: Preheat Oven. Preheat the oven to 400 degrees F (200 degrees C). Butter a 9×15-inch casserole dish.

Step 9: Mash Potatoes. Use a slotted spoon to remove the cooked potatoes to a bowl. Reserve the broth. Add the butter, salt, pepper, cayenne, and milk to the potatoes. Mix and mash until very smooth. Toss in ¾ cup of the Cheddar cheese and mix until incorporated.

Step 10: Assemble Pie. Pour the cabbage into the prepared casserole dish and press on it until nicely compacted. Evenly distribute and press the carrots over the cabbage. Place a nice, even layer of the sliced corned beef on top, overlapping the slices a bit and distributing the fatty pieces evenly until fully covered. Pour in 1 cup of the reserved broth.

Step 11: Add Potato Topping. Dollop the mashed potatoes over the top of the corned beef, then spread them into a uniform layer with the back of a spatula. Switch to a fork and push the potatoes to the edge of the dish to create a seal. Then, drag the fork sideways back and forth over the potatoes to create a textured surface.

Step 12: Add Cheese and Bake. Sprinkle with a little more Cheddar cheese. Bake in the center of the preheated oven until beautifully browned and piping hot, 45 minutes to 1 hour.

Step 13: Rest and Serve. Remove from the oven and let rest for 10 minutes. Meanwhile, warm any remaining broth over medium-low heat.

Step 14: Garnish and Serve. Cut the Shepherd’s Pie into squares and garnish with chopped scallions. Serve with the warmed broth.

These instructions are detailed and clear.