Preheat oven to 325°F. Coat an 8-inch square baking pan with cooking spray. Cut a 25- x 8-inch piece of parchment paper. Fold parchment rectangle in half (short end to short end), pressing firmly on folded end to make a crease. Fold creased end over about 3 inches, pressing firmly to make another crease in parchment paper. Unfold entire piece, and turn over. Pinch and pick up middle crease, creating a 3-inch-tall divider in middle of rectangle. Place in greased pan, pressing paper onto bottom of pan to fit as tightly as possible, and making sure divider is in the middle. Allow excess paper to extend over sides to use as handles. Coat top of parchment paper with cooking spray.
Beat butter, granulated sugar, and vanilla with an electric mixer at medium speed until well combined, about 1 minute. Beat in eggs and egg yolk. Add flour, baking powder, and salt to egg mixture; beat at medium speed until smooth, about 2 minutes. Remove 1 1/4 cups batter to another bowl, and stir in canned pumpkin and pumpkin pie spice. Spoon plain batter into 1 side of the parchment paper divider in prepared pan; spread until smooth. Spoon pumpkin batter into the empty side of the parchment paper divider of the prepared pan; spread until smooth.
Bake in preheated oven until a wooden pick inserted in center comes out clean, 30 to 33 minutes. Cool in pan 10 minutes. Lift cakes from pan, using paper sides as handles, and place on wire rack. Cool completely, about 30 minutes.
Remove cakes from parchment paper; trim the edges and tops of both cakes, as needed. Cut each loaf in half lengthwise, creating 4 equal strips.
Place jam in a microwave-safe bowl; microwave at HIGH just until warm, about 30 seconds. Spread jam on tops and sides of cake strips. Gently press 1 strip of each color together at long sides; top with remaining 2 strips, alternately stacking to create a checkerboard pattern.
Roll marzipan on a surface sprinkled with sifted powdered sugar into a 12- x 8-inch rectangle. Place cake loaf, top jam-side down, in center of marzipan rectangle with the short ends of loaf facing the long sides of rectangle. Brush remaining 3 sides of cake with jam. Wrap marzipan around cake loaf, and gently press to adhere. Trim ends and where seam meets. Place cake loaf on platter, seam side down. Brush surface of cake lightly to remove excess powdered sugar. Lightly score top of cake in a diamond pattern with the edge of a sharp knife.