Place a deep 13-14 inch cast iron skillet over medium heat. Add the ground beef, and sprinkle generously with salt and pepper. Break the ground beef into small pieces, with a wooden spoon, as it browns.
Once the ground beef is fully cooked, move it to the sides of the skillet. Add the onions, carrots, and garlic. Sauté for 5-8 minutes to soften the onions and carrots. (The carrots should be partially cooked before baking.)
Stir the mixture together. Then add in the frozen corn and pea, broth, tomato paste, Worcestershire sauce, mustard, cornstarch, and thyme. Mix well. Taste, then salt and pepper as needed.
Turn off the heat. Spread the mixture evenly over the bottom of the skillet.
Mix the shredded cheese into the mashed potatoes. (If using store-bought mashed potatoes, you may need to drain off the extra liquid or press the top with paper towels, before mixing in the cheese.)
Scoop the mashed potatoes over the meat filling and spread it to the sides of the skillet, making sure there are no gaps. Immediately place the cottage pie in the oven. Bake for 20-25 minutes, until golden on top.
Use ground lamb in place of ground beef to make a traditional Shepherd's Pie.