Spray a lidded container or glass bowl with cooking spray. Set aside.
In the bowl of a stand mixer fitted with dough hook, combine flour, graham cracker crumbs, sugar, yeast, and salt.
In a small saucepan, heat butter and milk until butter melts.
Remove from heat and allow to cool to 115℉/46℃.
With the mixer running, pour milk mixture into flour mixture.
Mix until mostly combined, about 1 minute.
Add egg.
Knead until dough is smooth, about 8-10 minutes. (Dough will not pull away from bowl.)
Scrape dough into prepared container.
Cover and let rise in a warm place until doubled in bulk, about 1½-2 hours. (You can also place uncovered in a proofing box set to 78℉ with water in the water tray.)