I would guess that many Southern cooks inherited tea cake recipes from their mothers or grandmothers.  I stumbled upon my family recipe and baked them recently.  I haven't tasted my mama's tea cakes in about 35 years since I was a young girl.
My mama would bake tea cakes often whenever we had a sweet tooth and didn't have anything else in the house. I'm embarrassed to say I thought they were a mediocre substitute for a bag of Chips Ahoy or some Duncan Hines something-or-another from a box.  
What do I think now after tasting them again?  I love the vanilla goodness, the buttery richness, and the simple, uncomplicated sweetness.  I love that this tea cake is part of my family's history. And I love that I think about my mom when I eat them.
Mama's Tea Cakes
½ cup butter
1 cup sugar
1 egg, well-beaten
1 teaspoon vanilla
¼ cup milk
2 teaspoons baking powder
2 ½ cups all-purpose flour
Cream butter for about 3 minutes.  Add sugar gradually, egg, milk and flavoring.  Sift dry ingredients, and add to first mixture.  Roll mixture out on lightly floured surface to about ¼ inch thickness.  Cut with round cutter (approximately 3 inches).  Bake on a greased or parchment-lined pan at 375 degrees for 10 minutes. Makes about 15 cakes.

