Preheat the oven to 325 degrees F. Line an 8x8-inch or 9x9-inch baking pan with parchment paper.

Combine melted butter, oil, and brown sugar in a large bowl and whisk to combine. Add egg and whisk until evenly incorporated. Mix in pumpkin puree and vanilla, then whisk in milk.

Add baking powder, baking soda, salt, and spice; whisk until evenly combined.

Add half of the flour mixture and mix gently. Once mostly incorporated, add the remaining flour and chopped pecans; fold in gently.

Pour batter into the prepared pan and spread it out evenly. Bake for 25-30 minutes until a skewer comes out clean. Transfer the cake to a wire rack to cool.

Combine softened cream cheese, softened butter, powdered sugar, and vanilla in a medium bowl and beat with an electric hand mixer until smooth and creamy. Spread the frosting evenly over the cooled cake and top with extra toasted pecans.