In a bowl, with a mixer on high speed, beat butter and sugar until smooth. Add egg and beat well. Beat in orange juice.
In another bowl, mix flour, orange peel, baking powder, salt, and baking soda. Stir half the flour mixture into the butter mixture, then the buttermilk, followed by the rest of the flour mixture, until just incorporated. Spoon batter equally into 24 buttered miniature muffin cups or 12 regular muffin cups (1/3 cup).
Bake in a 350° regular or convection oven until tops are lightly browned and a wooden skewer inserted into the center of one muffin comes out with moist crumbs attached, 20 to 25 minutes. Invert pan to remove cakes. Serve warm, or let cool to room temperature.
Nutritional analysis per tea cake.