Slice ends off tomatoes and cut slices 1/4 in thick.
On a plate, mix flour, Parmesan, and celery salt with fork until well blended.
Dip tomato slices in milk and then in the flour mixture.
Heat a frying pan over medium low heat until hot. Even with non stick pan you need to add oil, or the flour will burn and make a gigantic mess. (I have one of those ceramic coated pans and I only have to add a tiny amount of oil, but I have to add about a teaspoon every batch of tomato slices because otherwise the flour will brown before the tomato is cooked.)
Add floured tomato slices to oiled pan and allow to cook about 3 minutes per side. You will be able to tell when the tomato is done because piercing with a fork will have no hindrance. If the flour mixture is a dark brown color, but the tomato isn't soft, the heat is too intense and you need to turn to a lower setting or add more oil.