Preheat the oven to 350°F. Line a 9x9-inch square baking pan with parchment paper allowing a 2-inch overhang at each side.
Make the cake batter. Combine melted butter, sugar and vanilla extract in a large mixing bowl and whisk until pale and fluffy-looking. Whisk in eggs one at a time until very light and creamy. Mix in sour cream.
Sift flour, baking powder, baking soda and salt into a medium bowl and whisk to blend evenly. Add it to the wet ingredients and fold it in by hand with a spatula until mostly incorporated. It will still look a bit dry and very thick at this point. Before it is all incorporated, pour in the milk and fold it in until evenly combined and the batter is homogeneous. Add chocolate chips and fold them in.
Scrape the batter into the prepared pan and spread it out evenly. Scatter the raspberries on top and don’t press them in. Bake for 35-40 minutes until the top is just lightly golden and the cake feels firm to the touch. A toothpick inserted into the center should come out clean. Transfer to a wire rack and let cool for at least an hour. Enjoy slightly warm or at room temperature. Dust with icing sugar before serving.