Preheat the oven to 170 ° C / 350 ° F, grease and flour a bundt cake mold.
In a large bowl, beat eggs with sugar until frothy. Add zest, lemon juice, and oil and beat until everything is incorporated.
In a small bowl, mix flour, pepper, ginger, salt, baking soda, and baking powder. Add the flour and buttermilk to the egg mixture a little bit at a time. Mix well.
Pour the batter into the pan and bake for 40 to 50 minutes or until a toothpick comes out clean when poking the cake.
Remove from the oven and leave in the pan for 10 minutes before removing and letting cool on a rack.