Preheat the oven to 350°F (175°C).
Prepare the lemon slices by washing and thinly slicing the Meyer lemons, removing any seeds.
In a 9-inch round cake pan, melt the butter over low heat, then sprinkle the brown sugar evenly over it.
Arrange the lemon slices over the butter-sugar mixture in the pan, overlapping slightly if necessary.
In a large mixing bowl, beat the softened butter and granulated sugar until light and fluffy.
Add the eggs, one at a time, beating well after each addition, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, and salt.
Gradually add the dry mixture to the wet mixture, alternating with buttermilk, starting and ending with flour. Mix until just combined.
Pour the batter evenly over the arranged lemon slices in the cake pan.
Bake in the preheated oven for 35–40 minutes or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for about 10 minutes before inverting it onto a serving plate.
Serve warm or at room temperature, and enjoy your Meyer lemon upside-down cake!
