Preheat oven to 350°F (175°C). Grease and flour a 9-inch (22-23cm) round springform cake pan.
In a medium bowl, sift together 1 ½ cups all-purpose flour, 1 teaspoon baking powder, ¼ teaspoon baking soda and ¼ teaspoon salt. Reserve.
In a large bowl, cream together ½ cup unsalted butter, softened, and ¾ cup granulated sugar for about 3 minutes, until light and fluffy.
Add 2 eggs, one at a time, beating to incorporate after each addition. Add 1 teaspoon vanilla extract and mix.
Add the sifted dry ingredients to the butter mixture in 2 parts, alternating with ½ cup buttermilk, beginning and ending with the dry ingredients. Mix until just combined. Don’t overmix at this point or the cake will be tough. With a spatula, give the mixture a few folds to make sure it’s well integrated, and there are no dry spots in the bottom of the bowl.