Preheat the oven to 350°F (175°C).
Pour the melted butter into a 9-inch round cake pan and evenly sprinkle 3/4 cup granulated sugar over the butter.
Arrange the lemon slices in a single layer over the sugar and butter mixture in the pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, and salt.
In a large bowl, beat the softened butter and 1 cup granulated sugar together until light and fluffy, about 3 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the lemon juice, lemon zest, and vanilla extract until combined.
Alternately add the dry ingredients and the milk to the butter mixture, beginning and ending with the dry ingredients. Mix until just combined.
Pour the batter over the arranged lemon slices in the cake pan, spreading evenly.
Bake for 40 minutes or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and let it cool in the pan for 10 minutes.
Run a knife around the edges of the pan to loosen the cake, then invert the cake onto a serving plate.
Allow the cake to cool completely before slicing and serving.