**Preheat Oven:** Preheat to 350°F. Spray a 9x9-inch pan with non-stick spray and line with parchment paper.
**Mix Dry Ingredients:** In a medium bowl, whisk together flour, baking powder, baking soda, and salt.
**Cream Butter and Sugar:** In a large bowl, cream the butter and sugar with an electric mixer for 2 minutes until fluffy.
**Add Eggs and Vanilla:** Mix in eggs and vanilla on medium speed until smooth and pale, about 1 minute.
**Combine:** Gradually add dry ingredients and buttermilk, mixing on low speed until combined. Fold in lemon zest.
**Bake:** Pour batter into the prepared pan and bake for 35-40 minutes, or until a toothpick comes out clean.
**Cool:** Let the cake cool completely in the pan on a wire rack.