Preheat oven to 350 degrees F (175 degrees C).
Butter a 10" springform pan and add parchment paper to the bottom for easy removal.
Melt butter and milk together on the stove. Let the mixture cool a bit, until it's not burning hot but just a bit warm - you can continue to prep the topping + fruit while it cools a bit!
Combine brown sugar, butter, a pinch of salt, and a tiny splash of water together in a pot on the stove. Heat over low heat and stir together, just until the butter melts and everything combines. Set aside while you work on preparing the fruit.
Make sure to wash the fruit you are using - we've found that plums, peaches or apricots work well! Cut your stone fruit in half and remove the pits. Set aside while you work on the cake batter.
Combine flour, baking powder, and salt in a separate bowl.
Beat eggs and sugar together, either in a stand mixer with the whisk attachment, with a hand mixer, or by hand with a whisk.
The eggs and sugar should about double in volume and become light in color and a little bit thicker than liquid. When you lift the whisk out of the mixture, the mixture that flows back into the bowl should sit on the surface for just a second before sinking back in - that's ribbon stage, and it should be ready for the next step!
Add the vanilla extract to the eggs and sugar and mix together.
Now you are going to add your cooled wet ingredients and dry ingredients into the fluffy egg mixture in batches. You can do this by hand or with a paddle/whisk attachment on your stand mixer. First, sift in half of the dry mixture and fold together gently or run the mixer for just 10-15 seconds on low.
Then, add half of the wet mixture and fold together gently, or run the mixer for another 10-15 seconds on low. If you see dry ingredients stuck on the sides of the bowl, make sure to use a spatula to fold it in.
Repeat the process of sifting in the rest of the dry ingredients, mix, then add the rest of the wet ingredients and mix together, either by folding the ingredients together or running the mixer.
Finally, fold everything together a few times at the end until you have a smooth cake batter, making sure nothing is stuck on the sides or the bottom of the stand mixer bowl.
Pour the brown sugar mixture into the bottom of the prepared cake pan and spread across evenly. If it has hardened since sitting, you can heat it up a little bit to get it to be spreadable!
Arrange the fruit with the cut side down across the bottom. You can cut some of the halves into quarters for the edges!
Pour the cake batter over the fruit, making sure it's distributed evenly and covers the fruit.
Bake for 35-40 minutes on the center rack in the oven. You may want to check it after 30 minutes, depending on how hot your oven runs. When you test the cake with a knife or a cake tester, it should come out clean.
Remove from the oven and let cool for about 10-15 minutes. We like to leave it for a little bit just so that we don't deflate the cake immediately by turning it upside down.
After 10-15 minutes, remove the edge of the springform.
Turn the cake upside down, removing the parchment paper from the bottom. It should be nice and golden but not burnt! Let cool for at least another 15 minutes, but this cake it quite delicious enjoyed slightly warm with some ice cream. Slice and enjoy!