Preheat your oven to 350°F. Lightly grease an 8" square or 9" round pan that's at least 2" deep.
Whisk the dry ingredients together in a medium-sized bowl. Whisk the vanilla, vinegar, vegetable oil, and water in a separate bowl. Pour the wet ingredients into the bowl of dry ingredients, stirring until thoroughly combined. Pour the batter into the prepared pan.
Bake the cake for 30 to 35 minutes, until a toothpick inserted into the center comes out clean, or with a few moist crumbs clinging to it.
Serve the cake right from the pan; warm from the oven, it's wonderful with a big glass of milk.
Tips
Want to make this cake into cupcakes? Portion the batter into a standard (12-cup) muffin pan lined with lightly greased papers; you'll use a scant 1/4 cup batter (about 58g) in each. Bake for 18 to 20 minutes (22 minutes if you're baking with Gluten-Free Measure for Measure Flour) in a preheated 375°F oven, until a toothpick inserted into one of the center cupcakes comes out clean. Remove from the oven and cool on a rack. Frost with the frosting in step #5 above, if desired.