Preheat the oven to 400 degrees F.
Grease two large (14-by-16-inch) cookie sheets with shortening.
Sift together the flour, baking soda and salt. Using an electric mixer set to medium speed, cream the butter and sugar together. Add the eggs and vanilla. Add the sour cream and mix well. On low speed, gradually add the flour mixture until just blended. Turn the dough out onto a lightly floured board, and gently pat with floured hands to a 1/4-inch thickness. Cut with a 2-inch round, floured cookie cutter and place about 1 inch apart on the cookie sheets. Bake until the teacakes are lightly browned, about 10 to 12 minutes. Do not overbake. Sprinkle with a couple of tablespoons of sugar and remove the cookies to a rack to cool.
The dough is sticky, but be careful about adding too much extra flour when shaping the teacakes. By using care, patience, and a floured egg turner when patting and cutting, you will be rewarded with tasty, tender teacakes.
Adapted from Home Cooking with Trisha Yearwood (c) Clarkson Potter 2010