Peel the potatoes and roughly chop. In a medium pot, cover the potatoes with water and bring to a boil. Once boiling, reduce the temperature so that the potatoes are at a simmer. Simmer for about 10 minutes or until potatoes are soft.
While the potatoes cook, finely chop the onion and slice the carrots. Cook the onion and carrots in a large skillet on medium heat in a tablespoon of vegetable oil until the onions are soft. Add the crushed clove of garlic and continue to cook for about 1 minute.
Add the corned beef to the skillet, along with the frozen corn kernels. Mix and cook until warmed through.
Sprinkle the flour into the corned beef mixture. Toss to combine. Add 1 cup of beef broth and stir to combine. Bring the mixture to a simmer and allow to cook until the mixture becomes gravy-like.
When the potatoes are done, drain them. Return them to the pot and mash them. You can follow your usual mashed potato routine here, but we added about 1 tablespoon of butter and a half cup of milk. Set the mashed potatoes aside.
When your mashed potatoes and your beef mixture are both ready to go, it's time to assemble the shepherd's pie. Pour the beef mixture into an 8x8" glass pan and smooth it out with a spatula. Top the beef with the mashed potatoes and smooth them out as well.
Bake the shepherd's pie for 15 minutes in a 350 degree oven, or until the beef mixture is boiling. To brown the top, broil the pie for about 5 minutes or until the potatoes are browned.
Remove from the oven, allow to sit for at least 5 minutes, serve and enjoy!