Preheat oven to 400°F and Grease 2 ½ qt. casserole dish.
Heat the olive oil over medium-high heat in a large sauté pan. Place the sliced carrots in the pan and cook until tender.
Add your onions to the carrots and cook for 5 minutes till when the onions start to turn translucent.
Now add your beef and seasonings. Cook until the beef is fully cooked. and browned.
Drain the meat mixture and place back in the pan. Add the butter and peas; and place back on the stove on medium heat.
Stir the mixture until the butter is melted. Sprinkle with flour and stir until combined.
Add tomato paste, red wine and Worcestershire sauce. Toss to combine.
Add the chicken broth. Once the mixture thickens remove from heat.
Transfer the mixture to your 2 ½ qt. baking dish.
Make the mashed potatoes according to instructions. Scoop the potatoes and spread evenly on top of the meat mixture.
Brush the beaten egg on top of the mashed potatoes.
Top with Parmesan cheese. Bake for 20 minutes. Enjoy!