Heat a large skillet (I prefer nonstick here) over medium high heat, then add beef. Brown beef until fully cooked, about 5 minutes. Soak up excess beef fat with a paper towel, then add onion and carrots. Season with a pinch of salt and pepper, then cook for 10 minutes, until soft.
Add the peas and corn, and cook for 2 minutes. Add butter to the pan and toss around until fully melted, then stir in flour, thyme leaves, and garlic. Stir for 1 minute, until flour disappears. Add beef stock, then bring liquid to a boil over high heat. Cook for a minute or two until broth thickens into a light sauce. Remove pan from heat and transfer beef and veggie mixture to an 8x8 baking dish.
Preheat oven to 425°F.
To make the mashed potatoes, place mashed potatoes in a bowl, mix in shredded cheese until combined. Season with salt and pepper as desired. Spread potato mixture on top of veggie mixture.
Place baking dish on top of cookie sheet with sides (in case liquid overflows) place in preheated oven. Bake shepherd's pie for 20-25 minutes, until mashed potatoes are golden brown and crispy on top. Serve and enjoy!