A couple of notes, I used slightly less sugar called for than what I wrote here. Also, I checked my cake at the 20 minute mark and it was just about done so I didn't keep it in the oven for too much longer. The pick came out clean although in the picture, there appears to be batter in the center of the slice. For this small batch, it is probably easier to do the mixing by hand with a whisk. This cake is best slightly warm on the day it's made.
Makes 1 4.5-inch cake
1/2 cup all-purpose flour
1/4 teaspoon baking powder
1/4 teaspoon baking soda
1/8 teaspoon salt
2 tablespoon butter, softened
1/3 cup plus 1 teaspoon sugar, divided
1/4 teaspoon pure vanilla extract
1 egg
1/4 cup well-shaken buttermilk
1/2 cup fresh strawberries, halved
Preheat the oven to 400 degrees with rack in the middle. Butter and flour a 4.5-inch round cake pan.
Whisk together the flour, baking powder, baking soda, and salt.
Beat butter and 1/3 cup sugar with an electric mixer at medium-high speed until pale and fluffy, about 2 minutes, then beat in vanilla. Add egg and beat well.
At low speed, mix in flour mixture in three batches, alternating with buttermilk, beginning and ending with flour, and mixing until just combined.
Spoon batter into cake pan, smoothing top. Scatter the strawberries evenly over the top and sprinkle with the remaining sugar.
Bake until the cake is golden and a wooden pick inserted into center comes out clean, 20-30 minutes. Cool in the pan 10 minutes, then turn out onto a rack to cool to warm, 10 more minutes.