Microwave the milk in a microwave-safe container in 20-second increments until it reaches a temperature between 105-110℉. It should be warm but not hot. Add the warm milk, yeast, and sugar to the bowl of a stand mixer. Cover with a kitchen towel and let sit for 5-10 minutes. It will be bubbly and foamy when it is active and ready to use.
Add the eggs, vanilla extract, butter, flour, and salt to the milk mixture in a stand mixer fixed with a dough hook attachment. Knead for 7-10 minutes on medium speed. The dough is done when you press your finger into it and it doesn't stick to your fingers. If you find the dough is still sticky, add an extra tablespoon or two of flour and knead for a minute or two longer. Form the dough into a ball. Cover the ball of dough with a kitchen towel and let rise for 2 hours in a warm place.
While the dough is rising, work on the filling. First, crush the graham crackers into a fine crumb either using a food processor or by crushing them in a Ziploc bag with a rolling pin. Set aside.
Make the filling: In a large mixing bowl, use an electric mixer to cream together the butter and cream cheese for 2 minutes. Then add the vanilla extract and powdered sugar. Use a rubber spatula to scrape the sides of the bowl until there is no more dry sugar and the filling is nice and creamy. Set aside.
The dough is ready when it has doubled in size. Gently punch the dough down and remove it from the bowl onto a clean, lightly floured surface.
Roll the dough out on the floured surface into a 12"x18" rectangle. Spread the cream cheese mixture evenly over the top of the dough. Sprinkle the graham cracker crumbs evenly over the cream cheese mixture.
Preheat oven to 350℉. Chop the strawberries up into small pieces and sprinkle them over the cream cheese mixture and graham cracker crumbs.
Roll the dough tightly length-wise into a long tube. Use a serrated knife or a piece of unflavored dental floss to slice the dough into 12 rolls. Put them in a greased 9x13 baking dish and bake for 25-35 minutes. The rolls will be golden brown on top and the middle of the rolls will be baked fully and no longer doughy.
Make the frosting: With an electric mixer, cream together the cream cheese and butter in a large bowl. Add the vanilla extract, lemon juice, and powdered sugar. Then, mix in the chopped strawberries. You'll mix until the frosting is whipped and creamy and the strawberries are slightly broken up into the frosting. Spread over the rolls and serve immediately. Enjoy!