Prepare the Dough:

1. In a large bowl, combine warm milk and granulated sugar. Sprinkle active dry yeast over the top and let it sit until foamy, about 10 minutes.
2. Add melted butter, egg, and salt to the yeast mixture. Gradually mix in all-purpose flour until a soft dough forms.
3. Knead the dough on a lightly floured surface for about 5 minutes, until smooth and elastic.
4. Place the dough in a greased bowl, cover, and let it rise in a warm place until doubled in size, approximately 1 hour.

Prepare the Filling:

1. In a medium bowl, beat softened cream cheese, granulated sugar, and vanilla extract until smooth.
2. Gently fold in diced fresh strawberries and crushed graham crackers.

Assemble the Rolls:

1. Roll out the risen dough on a floured surface into a 9×16-inch rectangle.
2. Spread the cream cheese and strawberry filling evenly over the dough, leaving a small border around the edges.
3. Starting from the long side, tightly roll up the dough into a log.
4. Cut the log into 12 equal pieces and place them in a greased 9×13-inch baking dish.
5. Cover the dish with a clean kitchen towel and let the rolls rise for an additional 25 minutes.

Bake the Rolls:

1. Preheat the oven to 375°F (190°C).
2. Bake the rolls for 15 to 18 minutes, until they are lightly golden brown.

Prepare the Glaze:

1. While the rolls are baking, beat softened cream cheese and unsalted butter together until creamy.
2. Add powdered sugar, pureed fresh strawberries, lemon juice, and vanilla extract. Mix until smooth and well combined.

Glaze the Rolls:

1. Once the rolls are out of the oven, let them cool slightly before spreading the strawberry cream cheese glaze over the top.