Heat the oven to 350F and line a 9x13 pan with parchment, leaving overhang on the sides.
Stir the melted butter, brown sugar, flour, baking powder, salt, and cinnamon together until the mixture clumps. Press it firmly and evenly into the pan.
Mix the Pumpkin Layer
Whisk the pumpkin puree, granulated sugar, egg, pumpkin pie spice, and vanilla until smooth. Spread it over the pressed base in an even layer.
Bake
Bake for 30 to 35 minutes, until the pumpkin layer is set and no longer wobbly in the center. Cool the pan on a rack.
Make the Caramel and Chill
Melt the butter in a small saucepan over medium heat until it smells nutty and turns golden, about 4 to 5 minutes. Stir in the brown sugar and heavy cream and let it bubble gently for 2 minutes, then stir in the salt.
Pour the warm caramel over the cooled bars and spread to the edges. Finish with flaky salt if using. Chill at least 2 hours, then lift out and cut into 16 squares.
Notes
Chill before cutting: Cold bars give clean, bakery-style edges. Warm caramel smears.
Use pure pumpkin: Not pie filling, which is pre-sweetened and pre-spiced.
Don't overcook the caramel: Pull it at the 2-minute bubble or it sets hard.
Make ahead: Bake and chill a day early, then cut just before serving.