In the bowl of a stand mixer fitted with the paddle attachment, beat butter and brown sugar at medium speed until creamy, 2 to 3 minutes, stopping to scrape sides of bowl. Beat in molasses and vanilla.

In a medium bowl, whisk together flour, graham cracker crumbs, cinnamon, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined.

Turn out dough, and shape into a disk. Wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.

Preheat oven to 350°F (180°C). Line baking sheets with parchment paper.

Divide dough into 12 portions (about 60 grams each). Roll each portion into a ball, slightly flatten, and lightly dust with flour. Using a well-floured cookie press, press each ball until edges of dough slightly exceed diameter of press. Gently pull dough off press. (See Note). Using a 2/-inch round fluted cutter dipped in flour, cut pressed dough without twisting cutter. Place 2 inches apart on prepared pans. Using a pastry brush, gently brush off excess flour from cookies. Repeat rolling, pressing, and cutting dough scraps to use all dough.

Bake until bottom edges are very lightly browned, 10 to 12 minutes. Let cool completely on pans on wire racks. Store in an airtight container for up to 4 days.