Preheat the oven to 350°C. grease an 8-inch square pan and line it with parchment so that the paper comes up the sides of the pan.
For the crust, using a food processor, pulse the flour and brown sugar together, then cut in the butter until evenly blended (the mixture will be dry and crumbly). Alternatively, this base can be made by hand, blending the butter into the flour and sugar using a pastry cutter. Press this into the prepared pan and bake it for about 18 minutes, until it turns just a little brown at the edges. Cool while making the filling.
Beat the cream cheese to soften and then beat in the sugar. Add the pumpkin and stir until smooth. Switch to a whisk and add in the flour, baking powder and cinnamon. Whisk in the egg and egg yolk and set aside.
For the cheesecake swirl, beat the cream cheese until smooth and then beat in the sugar. Stir in the egg yolk and vanilla until smooth.
Pour the pumpkin cheesecake onto the cooled crust. Either spoon or pipe the cheesecake swirl on top and use a bamboo skewer to create pretty swirls. Bake for about 30 minutes until, like a cheesecake, the filling is set at the edges but still has a little jiggle at the centre. Cool the squares to room temperature, then chill for at least 2 hours before slicing.
The squares will keep, refrigerated, for up to 3 days.