First, preheat the oven to 350°F. Cream ½ cup butter and one cup granulated sugar with an electric mixer until smooth in a large mixing bowl.
Next, add the eggs, milk, and vanilla extract and mix on low until no clumps remain and the egg yolks are incorporated.
Then, combine the flour and baking powder in a medium bowl with a whisk, and then add the flour mixture to the cake batter.
Fold the dry ingredients into the batter with a spatula until they are fully incorporated.
Grease the inside of a 9-inch round cake pan with the remaining two tablespoons of butter, making sure to get the sides of the pan. Sprinkle the remaining ¼th cup of sugar on top of the butter on the base of the cake pan. Then, slice the oranges into ¼-inch slices and place them in a single layer over the sugar.
Pour the cake batter over the orange slices and bake for 40 minutes, until golden brown on top and a toothpick inserted into the middle comes out clean.
Allow the cake to cool slightly while preparing the glaze by whisking the orange juice and powdered sugar together until smooth.
Then, place a wire rack or a cake platter inverted on top of the cake pan. With one hand on the platter and one hand on the pan, carefully turn them over simultaneously, so the cake pan faces upside down on top of the platter or rack. Gently lift the pan, and the cake should slide out easily. Drizzle the orange upside-down cake with the citrus glaze. Allow the cake to cool completely before serving.