Preheat the oven to 350 degrees F. Line the bottom of a 9-inch round cake pan with a parchment round.
Pour the melted butter into the pan and sprinkle the brown sugar evenly over it. Arrange the pecan halves in a single layer, flat side up, in whatever pattern you want on the finished top.
Mix the Batter
Whisk the flour, baking powder, salt, and pumpkin pie spice in a bowl.
In a separate bowl, cream the softened butter and granulated sugar until fluffy. Beat in the eggs, pumpkin puree, and vanilla until smooth.
Add the dry ingredients in two additions, alternating with the milk, and mix just until combined. Spoon the batter gently over the pecans and spread it level without disturbing them.
Bake and Flip
Bake for 40 to 45 minutes, until a toothpick inserted in the center comes out clean.
Let the cake rest for 10 to 15 minutes only. Set a serving plate over the pan, flip in one confident motion, lift the pan away, and peel off the parchment. Let the caramel settle before slicing.
Notes
Flip while warm: wait longer than 15 minutes and the caramel sets and sticks.
Line the base: a parchment round is cheap insurance against a stuck top.
Arrange pecans first: the bottom layer is your finished top, so lay them out neatly.
Drain fresh puree: homemade pumpkin should be thick, not watery.