Preheat the oven to 325°F. Line a 12x17x1 inch baking pan (also known as a jelly roll pan or half sheet pan) with buttered parchment paper or foil.
BROWNIE LAYER
Melt butter and chocolate in top of double boiler (or carefully, in short bursts, in the the microwave). Set aside to cool slightly.
In a large bowl, whisk 6 eggs, brown sugar, and 1½ cups granulated sugar together. Stir in vanilla, salt, melted butter and chocolate chocolate mixture, flour and cocoa. Pour into prepared pan and spread to the sides.
CHEESECAKE LAYER
Beat the cream cheese using a mixer on medium speed until fluffy. Add remaining eggs, sugar, vanilla and cornstarch; beat until smooth.
Dollop mixture all over the chocolate layer. Gently use a spoon to spread out evenly over the chocolate, trying not to dig into the chocolate layer. (If you're patient, it works out just fine.)
PUMPKIN LAYER
Whisk together jam and pumpkin butter in a small bowl.
Drop spoonfuls onto cream cheese layer and draw swirls using a knife. Try to stay inside the cream cheese layer only and don't pull up the chocolate with the knife.
Bake until center tests clean, about 40 minutes. Cool completely before cutting.
Notes
It's best to cool these to room temperature, then wrap with plastic wrap and refrigerate overnight before cutting. You'll get the cleanest cuts that way.
If you prefer, you can use Halloween themed cookie cutters to cut out shaped brownies, but you'll have lots of tidbits leftover to munch on.