Preheat the oven to 425 F.

Heat a large skillet over medium heat and melt 1 tablespoon of the butter. Add the shallots, veggies and a pinch of salt and cook, stirring, until softened, 7 to 10 minutes. Transfer to a 9-by-9 casserole dish and spread out evenly.

To the skillet, add the beef and 1 teaspoon of salt and brown it, breaking up with a spoon or spatula. Use a slotted spoon to transfer the mixture to the casserole dish and spread it out evenly. Scatter on the tomatoes. Set aside while you make the creamed soup. Discard the juices that remain in the skillet, wipe it out, and return it to medium heat.

To make the creamed soup, melt the remaining 4 tablespoons of butter and whisk in the flour to make a paste. Cook, whisking, for 2 minutes. Whisk in the chicken stock very gradually, in 2 or 3 additions, while whisking continuously and allowing the mixture to thicken before adding each addition. Whisk in the milk very slowly in 2 or 3 additions, while whisking continuously and allowing the mixture to thicken before adding each addition. Season with a bunch of turns of black pepper, thyme, and mustard, and reduce the heat and simmer for 5 minutes, whisking occasionally. Taste and add salt if desired.

Pour or ladle the mixture over the ground beef. Top with cheese and one even layer of potatoes. Season the potatoes with salt and pepper. Bake until the cheese is splotchy and the potatoes are cooked through; begin checking at 35 minutes.

Top with flaky salt and parsley, if desired. Serve with ketchup, if desired.

To make ahead: Assemble in a metal dish (don’t bake). Let cool, wrap in plastic wrap or foil, and refrigerate or freeze until ready to cook. It'll last 2 days in the refrigerator and 3 months in the freezer. If reheating from the fridge, proceed as directed but add on a few more minutes in the oven to ensure that it’s heated through. To reheat from frozen, cover loosely with foil and bake at 350 F for an hour, and then uncover and increase the heat to 425 F and bake until the potatoes are splotchy and the innards are heated through; begin checking at 20 minutes. Let cool slightly, top with parsley, if desired, and serve with ketchup, if desired.