With a serrated knife, cut the graham cracker pieces as shown. Tip: To create the pairs, cut one piece, then use it as a guide for the second.
To assemble, use Vanilla Decorating Icing, or white chocolate chips, melted in a heat- safe bowl according to the package directions.
Spoon the icing or melted chips into a ziplock bag and snip off a corner. Pipe it along the house's seams and assemble as shown. Let the icing or candy set, then use more (reheat if needed) to attach sprinkles and other sweet decorations, and let it set.
To place the house on a stick, trim a piece of brownie to fit inside the house. Slide the brownie onto a lollipop stick, then carefully slide the house on top.
In a small bowl, whisk together the sugar, milk, corn syrup, and flavored extract until smooth.