Preheat your oven to 375°F (190°C) and grease an 8x8-inch baking dish with butter.

In a medium bowl, whisk together the flour, baking powder, and salt, then set aside.

In a large bowl, beat the softened butter and granulated sugar with a hand mixer until light and fluffy, about 2 to 3 minutes.

Add the egg and vanilla extract to the butter mixture, beating well until fully incorporated and smooth.

Gradually add the dry ingredients and milk in alternating batches, mixing on low speed just until a thick batter forms.

Spread the cake batter evenly into the prepared baking dish using a spatula.

In a small saucepan over medium heat, combine the maple syrup, heavy cream, and brown sugar, stirring until the sugar dissolves and the mixture is hot, about 3 minutes.

Carefully pour the hot maple cream mixture directly over the raw cake batter in the baking dish without stirring them together.

Bake for 35 minutes, or until the cake top is golden brown and a toothpick inserted into the center of the cake part comes out clean.

Let the pudding cool for 10 minutes before serving warm, spooning the rich caramel sauce from the bottom of the dish over each portion.