Cook the corn according to the package instructions. Drain and set aside.
Start the potatoes for the topping. Put them in a large pot with enough water to cover them by a couple of inches. Add about 2 teaspoons of salt to the water. Bring the potatoes to a boil, uncovered, over high heat. Cook them for 10 to 13 minutes. Meanwhile, make the meat filling.
Melt the butter in a large skillet over medium heat. Sauté the onion and celery in the butter, stirring often, for about 5 to 6 minutes.
Add the ground beef to the pan and break it up with a wooden spoon as it browns. Remove the skillet from the stove and, resting it on a heatproof surface so it won't feel so heavy, tilt the pan so that the excess fat runs to the side. Carefully spoon out the fat and discard it (this will make the dish leaner and healthier, as well as lighter tasting).
Put the skillet back on the burner and set the heat to medium low. Stir the garlic and flour into the beef mixture. Stir in the beef broth, then the canned tomatoes, then the herbs, reserved corn, and Worcestershire sauce.
Gently simmer the mixture for several minutes, partially covered, then add salt (1/4 teaspoon, give or take a little) and pepper to taste. Transfer the mixture to a large buttered casserole. Set the oven to 400°, and while it heats, check to see if your boiling potatoes are done.
To test the potatoes, use a slotted spoon to transfer a cube from the water to a cutting board and allow it to cool for 30 seconds or so. If you can slice through the chunk easily with a butter knife, the potatoes are done.
Set a large colander in the sink and drain the potatoes in it (this job can generate a lot of steam, so it is best done by an adult or under adult supervision). Transfer the drained potatoes to a large mixing bowl and scatter the butter pieces over them. Spoon the sour cream here and there over the hot potatoes as well. Wait several minutes for the butter to melt and the sour cream to warm so the ingredients will be easier to blend, then partially mash the potatoes with a hand masher.
Switch to an electric mixer set at medium speed and continue to mash, adding enough milk to make medium-soft mashed potatoes. Don't make them too soft, however; you want them to have some body.
Salt the potatoes to taste and spoon them evenly over the filling. Sprinkle the cheese over the top, then sprinkle on some paprika (be sure to wash your hands right afterward so you don't accidentally rub any of the spice in your eyes). Bake the pie on the center oven rack for about 20 minutes, until the top is golden brown. Cool for several minutes before serving.