Preheat the oven to 350F (180C).
Sift the flour into a mixing bowl, then add the brown sugar and baking powder and stir to combine.
Add all the other ingredients except the peaches, then whisk together until you have a smooth batter.
Remove the pits from the peaches. Cut 3 of them into small cubes and slice the other 3.
Fold the cubed peaches into the batter and mix evenly.
Grease a baking tin (I used a rectangular loaf/pound cake tin, about 30 cm long).
Pour in the batter and arrange the sliced peaches on top. Sprinkle a little brown sugar over the surface.
Bake for 25 minutes. Test with a toothpick inserted into the center: if it comes out clean, the cake is done. If not, bake for a few more minutes until set.
Let it cool before serving. I didn't wait, which is why it looks a bit fragile in the photos, but once fully cooled it holds together perfectly.