Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
Wash and halve the apricots, removing the pits. Set them aside.
In a large mixing bowl, cream together the softened butter and sugar until light and fluffy. This can be done using an electric mixer or by hand.
Add the eggs, one at a time, to the butter-sugar mixture, beating well after each addition. Make sure the eggs are fully incorporated before adding the next one.
In a separate bowl, whisk together the all-purpose flour, baking powder, and salt.
Gradually add the dry ingredients to the butter-sugar mixture, alternating with milk. Begin and end with the dry ingredients, mixing well after each addition.
Stir in the vanilla extract to the batter, ensuring it is thoroughly combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Arrange the apricot halves on top of the batter, cut side down, in a circular pattern. Press them slightly into the batter.
Place the cake pan in the preheated oven and bake for approximately 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for about 10 minutes. Then, transfer it to a wire rack to cool completely.
Serve the Apricot Cake as is or dust with powdered sugar for an extra touch of sweetness. Enjoy!