Heat the oven to 350°F (175°C) with a rack placed in the center.
Fit parchment paper into an 8 × 8-inch baking pan, leaving about 2 inches hanging over two sides for lifting.
Microwave the butter and chopped semi-sweet chocolate in 20-second intervals, stirring after each one, until completely smooth. Let it cool for about 3 minutes.
Whisk in the sugar. Add the eggs one at a time, then mix in the vanilla. Fold in the flour, cocoa powder, and salt until no dry streaks remain.
Beat the softened cream cheese until smooth. Mix in the sugar, pumpkin puree, egg yolk, vanilla, and pumpkin pie spice until creamy and evenly colored.
Reserve about ½ cup brownie batter. Spread the remaining batter evenly into the prepared pan.
Spoon the pumpkin cheesecake mixture over the brownie batter and gently spread it across the surface.
Place about 8–10 small dollops of the reserved chocolate batter over the cheesecake layer.
Drag a butter knife or skewer through the top layers in loose S-shaped curves. Make about 5–7 passes and stop while the chocolate and pumpkin colors are still clearly visible.
Bake at 350°F (175°C) for 38–45 minutes. The edges should be set and the center should still have a slight wobble. A toothpick inserted into a brownie section should have moist crumbs rather than liquid batter.
Leave the brownies in the pan on a wire rack for at least 1½ hours. For firmer slices, refrigerate them for another 30–60 minutes.
Lift the brownies out using the parchment handles and cut into 16 squares with a sharp knife. Clean the blade between cuts for neat edges.
