Mix the warm milk with the yeast and a teaspoon of sugar; let it sit for 5-10 minutes until it becomes foamy, indicating the yeast is active.
In a large bowl, combine the flour, crushed graham crackers, remaining sugar, melted butter, and egg. Pour in the activated yeast mixture and knead until the dough is smooth and slightly sticky, about 5-7 minutes by hand or using a mixer with a dough hook.
Cover the dough with a clean towel and let it rise in a warm spot for about 1 hour, or until it has doubled in size and feels puffy.
Meanwhile, beat the softened cream cheese with sugar and vanilla until creamy and smooth. Gently fold in the diced strawberries to create the filling mixture.
Once the dough has risen, punch it down to release the air and turn it onto a floured surface. Roll it out into a rectangle about 12x8 inches.
Spread the cream cheese and strawberry filling evenly over the rolled-out dough, leaving a small border around the edges.
Carefully roll the dough tightly from the long side into a log, sealing the edge underneath.
Using a sharp knife, cut the rolled log into 8 equal pieces and arrange them on a parchment-lined baking sheet, spacing them evenly.
Brush the tops of the buns with the beaten egg to give them a shiny, golden finish during baking.
Bake in a preheated oven at 375°F (190°C) for 18-20 minutes, or until the buns are golden brown and fragrant.
Remove from the oven and let the buns cool slightly before serving. Enjoy the warm, fruity, and creamy bites!
