Preheat your oven to 350°F (175°C).
Melt 1/2 cup of butter and pour it into the bottom of a greased 9-inch round cake pan.
Sprinkle 1 cup of sugar evenly over the melted butter.
Arrange the lemon slices over the sugar in a single layer.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a separate large bowl, cream together 1/2 cup of butter and 1 cup of sugar until light and fluffy.
Beat in the eggs, one at a time, then stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Mix until just combined.
Stir in the lemon zest.
Pour the cake batter over the arranged lemons in the pan, spreading it evenly.
Bake in the preheated oven for 40-45 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 15 minutes.
Invert the cake onto a serving plate, allowing the lemon topping to become the top of the cake.
Serve the Lemon Upside Down Cake slices warm or at room temperature.