Preheat the oven to 350.
Heat a 12" skillet over medium heat and add the ground beef, salt, pepper, carrots and onion breaking up the beef as it cooks until no pink remains. Drain almost all the fat except 1/4 cup.
Return the heat to medium, and add the garlic, tomato paste, worchestershire sauce, and the flour. Stir to combine (the mixture will be slightly pasty) and cook 1 minute until no raw flour is seen.
Add the beef broth, thyme and rosemary and turn the heat down to medium low. Simmer gently until the sauce begins to thicken, about 8 minutes or so.
Add the corn and peas and stir to combine. At this point you can cool the beef layer for assembly later, transfer it to an oven-safe dish if your skillet isn't oven safe, or simply add the potatoes and bake if it is oven safe.
Spread the potatoes over the beef and sprinkle with cheddar cheese and a grind of pepper.
Bake until the potatoes begin to brown on the edges and the dish is bubbling, about 35 minutes.