Preheat oven to 350 degrees F (175 degrees C). Line an 8-inch square cake pan with parchment paper.
Beat pumpkin puree, sugar, oil, eggs, pumpkin pie spice, and vanilla extract together in a bowl.
Sift flour, baking soda, baking powder, and salt into a bowl. Add to the pumpkin mixture; stir until just combined. Pour into prepared pan; smooth top with a spatula.
Bake in the preheated oven until a toothpick inserted into the middle comes out clean, 35 to 40 minutes.
Combine caramel sauce and 1 1/2 teaspoons bourbon in a saucepan over low heat; warm through, about 2 minutes. Poke holes evenly over the surface of the cake using a chopstick. Reserve 1 teaspoon of the caramel-bourbon mixture; pour remaining mixture over the cake. Place on cooling rack.
Beat cream and remaining 1 1/2 teaspoons bourbon in a bowl using an electric mixer until soft peaks form. Spoon whipped cream on cake; scatter pecans and drizzle reserved caramel sauce on top.