Preheat the oven to 350°F (175°C) and prepare the cake pan.
Slice the Meyer lemons thinly and arrange them in the bottom of the prepared pan.
In a saucepan, melt ½ cup of butter and 1 cup of sugar over medium heat until bubbly and slightly caramelized, then pour over the lemons.
In a mixing bowl, cream ½ cup of softened butter and ½ cup of sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition.
Sift together the flour, baking powder, and salt, then gradually add to the wet mixture.
Pour the batter over the prepared lemons and spread evenly.
Bake for 35-40 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan for 10 minutes, then invert onto a serving plate.
Dust with powdered sugar before serving, if desired.