In a medium bowl, mix together the flour, baking powder, salt, and lemon zest. Set aside.
In a large bowl, beat the butter and sugar until fluffy, around 3 minutes.
Beat in the egg until thoroughly incorporated. Then add the vanilla extract and lemon juice and mix. Slowly pour in the milk while mixing.
Add the dry ingredients to the wet ingredients and stir until combined. Then add in the berries and beat for another minute until incorporated.
Pour the batter into a 12-inch cast-iron skillet. Bake for 25-30 minutes, or until the edges are golden brown on top and a toothpick inserted into the center comes out clean.
In a small bowl, whisk together the powdered sugar, vanilla, lemon juice, and milk until smooth. Add more milk as needed until the glaze runs off your spoon. (If you prefer a vanilla glaze, leave out the lemon juice.)
Pour lemon glaze onto the cake and let sit for 5 minutes to soak in. Serve warm or at room temperature. I like to top the cake with some more fresh berries for garnish.
Notes
There is enough juice in 1 lemon for both the cake and glaze. Zest the lemon first, and then cut it in half for juicing.