Graham flour is available at bobsredmill.com. Find star-shaped cookie cutters at baking-supply stores or at cookiecutter.com.
Make the cookies: Whisk together flours, graham cracker crumbs, and 1 teaspoon salt in a medium bowl.
Beat butter and sugars with a mixer on medium speed until pale and fluffy. Add eggs, 1 at a time, and beat for 2 minutes. Reduce speed to low, and gradually add flour mixture. Beat until well combined, 2 to 3 minutes. Divide dough in half, and shape each half into a disk. Wrap in plastic wrap. Refrigerate until firm, at least 2 hours.
Preheat oven to 350 degrees. Roll out dough to a scant 1/4-inch thickness on a lightly floured surface. Cut out star shapes using a 3-inch cutter. Gently press a 2 1/2-inch star cookie cutter into the center of each to create an outline. Transfer cookies to parchment-lined baking sheets, spacing each 1 inch apart. Refrigerate for 15 minutes.
Bake cookies until pale gold, 12 to 15 minutes. Let cookies cool on sheets set on wire racks for 10 minutes. Transfer cookies to racks, and let cool completely.
Make the marshmallow filling: Cook sugar, corn syrup, and 3/4 cup water in a medium saucepan over high heat, stirring and brushing down sides of pan with a pastry brush to prevent sugar crystals from forming, until a candy thermometer reaches 260 degrees, about 10 minutes.
Meanwhile, sprinkle gelatin over remaining 3/4 cup water in a heatproof bowl, and let stand for 5 minutes to soften. Set bowl over a pan of simmering water, and cook, whisking constantly, until gelatin dissolves. Remove from heat. Whisk egg whites with a mixer on medium speed until soft peaks form.
Once sugar mixture reaches 260 degrees, immediately whisk gelatin mixture into saucepan (it will foam up). Reduce speed on egg whites to low, and gradually add sugar-gelatin mixture to egg whites. Raise speed to high, and beat until mixture is thick, about 10 minutes.
Transfer half of the marshmallow filling to a disposable pastry bag or a resealable plastic bag, and snip a 1/4-inch opening. (Leave remaining marshmallow in bowl with mixer on low speed.) Immediately, pipe marshmallow around edges of half of the cookies and fill in centers, then top with another cookie, pressing lightly. Dip edges of cookies into coconut to coat. Repeat with remaining marshmallow filling, cookies, and coconut.
Dough can be refrigerated for up to 1 week and frozen for up to 1 month. Thaw before using. Unfilled cookies can be stored at room temperature for up to 4 days. Sandwiched cookies can be stored at room temperature for up to 2 days.