Preheat oven to 350°F (175°C).
Grease and line an 8-inch round cake pan.
In a bowl, whisk flour, sugar, baking powder, and salt.
In another bowl, mix eggs, melted butter, milk, and vanilla extract.
Pour wet ingredients into dry ingredients and mix until just combined.
Gently fold in chopped apricots.
Pour batter into prepared cake pan.
Sprinkle brown sugar evenly on top.
Bake for 35–40 minutes until a toothpick inserted comes out clean.
Cool completely before slicing.
Dust with powdered sugar before serving if desired.