Preheat the oven to 350°F (175°C). Thoroughly grease a 9-inch bundt or round cake pan and line the base with a round of parchment paper.

In a small saucepan over medium heat, combine the butter, brown sugar, and maple syrup. Stir until fully melted and the mixture begins to bubble smoothly, about 2 minutes. Immediately pour into the prepared cake pan, spreading evenly across the bottom.

Arrange the pecan halves gently over the warm caramel layer in an even single layer.

In a separate mixing bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.

In a large bowl, use an electric mixer to beat the softened butter and granulated sugar together until pale and fluffy, about 2 minutes. Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract.

Add half of the dry mixture to the creamed butter and sugar, blending just until combined. Then mix in the sour cream and milk. Add the remaining dry ingredients and stir gently until just incorporated. Do not overmix.

Spoon the prepared cake batter over the pecan-caramel layer, smoothing the surface with a spatula for an even finish.

Bake for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.

Allow the cake to cool in the pan for 10 minutes. Run a knife carefully along the edges to loosen, then invert the cake onto a serving platter while still warm. Gently peel away the parchment to reveal the glossy, golden pecan topping.