1. Brown the beef in a large pan and transfer to a bowl (or put it in the baking pan you’re going to use; no point in getting another bowl dirty).
2. Add the onions, celery, mushrooms, and oil to the pan and cook over medium-high heat, stirring frequently, until the vegetables turn brown, 10 to 15 minutes.
3. Add the peas and carrots, then stir in the flour to combine. Stir in the broth and salt and pepper; cook while stirring until the mixture thickens. Add the beef back in the pan and mix well. Turn the mixture into a 9×13-inch pan and spread it evenly.
4. Adjust the oven rack to the middle position and preheat the oven to 425 degrees Fahrenheit.
5. In a food processor, process the onion and oil until smooth. Add the eggs and salt and pepper and process a few more seconds until combined. Pour the mixture into a mixing bowl and switch to the grating blade (not the shredding blade). Grate the potatoes and add them to the bowl. Mix well and pour the batter over the beef mixture.
6. Bake for one to one and a half hours, until the top is golden brown.