Heat the milk in a saucepan until it begins to bubble, then remove from heat.
Stir in butter until melted and let the mixture cool to lukewarm.
In a large mixing bowl, whisk together 2 1/4 cups flour, yeast, sugar, salt, and lemon zest.
Add the egg and lukewarm milk mixture, stirring with a wooden spoon.
Gradually add the remaining flour, 1/2 cup at a time, stirring well after each addition until the dough comes together.
Transfer the dough to a lightly floured surface and knead until smooth, about five minutes, or use a stand mixer with a dough hook.
Cover with a damp cloth and let it rest for 10 minutes.
Roll out the dough into a 12x9-inch rectangle on a floured surface, using a 9x13-inch baking dish as a guide.
Spread strawberry compote evenly over the dough, extending to the edges.
Sprinkle cinnamon on top if desired.
Slice the dough into 12 strips, roll them up, and place them in a baking pan.
Cover and let the rolls rise in a warm place until doubled in size, about 45 minutes.
Meanwhile, preheat the oven to 350°F (190°C).
Bake the rolls for 23-25 minutes until golden brown, then let them cool for 10 minutes before adding fresh strawberry slices and spreading with frosting.
To make the frosting, beat softened butter and cream cheese until smooth using an electric mixer.
Mix in strawberry compote, then gradually add powdered sugar, 1/2 cup at a time, beating until creamy.
Adjust consistency with heavy cream or milk as needed.
Serve warm.