Preheat the oven to 400°F.
In a skillet, heat up a bit of oil over medium high heat. Add the onion and carrots and cook until slightly softened. Remove from the pan and set aside. Add a bit more oil to the pan and cook the beef until deeply browned. Drain off excess fat, if needed. Stir in the onions, carrots, and frozen peas. Taste and season with salt and pepper. Spoon the beef mixture into a oven proof dish and set aside while making the macaroni and cheese.
Cook the pasta according to the package, drain and set aside.
Over medium heat, melt the butter. Add the flour and stir constantly over medium heat for about three minutes, until smooth. Pour in half of the milk in a thin stream while whisking. When smooth, add the rest of the milk. Keep on medium heat and stir for about 10 minutes, until the sauce thickens. Taste and season with salt and pepper. Stir in 1 cup of cheddar. Add the drained macaroni and stir to coat.
Top the beef and sprinkle on the remaining 1/2 cup of cheese. Bake until cheese is melted and bubbly, about 15-20 minutes. Enjoy warm.