Begin by chopping the onion and dicing the carrots.
Heat the large saucepan over medium heat and add the ground beef. Use a wooden spoon to break it up as it cooks. Incorporate the onions after a couple minutes.
Add diced carrots to the beef and onion mixture.
Sprinkle the flour over the beef and vegetables, stirring continuously to create a roux. Slowly pour in the beef broth, whisking as you go to prevent lumps from forming. Add the milk.
Introduce the frozen peas into the thickened soup base. Season the mixture.
Stir the mashed potatoes into the soup, folding them carefully. Taste and re-season if needed.
Notes
This soup can be stored in an airtight container in the fridge for up to 3 days. To freeze, consider keeping the mashed potato component separate.