Make the Strawberry Filling: In a saucepan, combine strawberries, brown sugar, and lemon juice. Cook over medium heat, stirring occasionally, until the strawberries release their juice and soften. In a small bowl, whisk together cornstarch and water to make a slurry. Add the cornstarch mixture to the strawberries and stir until thickened. Remove from heat and let cool.

Make the Tangzhong: In a small saucepan, whisk together flour and water. Heat over medium-low heat, whisking constantly, until the mixture thickens and forms a paste. Remove from heat and let cool.

Make the Dough: In a large bowl, combine flour, sugar, yeast, and salt. Add warm milk, egg, vanilla, and cooled tangzhong. Mix until the dough starts to come together. Knead in softened butter and continue kneading the dough for about 8-10 minutes until smooth and elastic. Cover the dough with a damp cloth and let it rise in a warm place for 1–2 hours, or until doubled in size.

Assemble the Rolls: Punch down the dough and roll it out on a floured surface into a rectangle (about 12×18 inches). Spread the cooled strawberry filling evenly over the dough, leaving a small border around the edges. Starting from one edge, roll the dough tightly into a log. Slice the log into 12 equal pieces and place them in a greased 9×13-inch baking dish. Cover and let the rolls rise for another 30–45 minutes until puffy.

Bake the Rolls: Preheat your oven to 350°F (175°C). Bake the rolls for 25–30 minutes, or until golden brown on top.

Make the Glaze: In a medium bowl, beat together cream cheese and butter until smooth. Add powdered sugar, reserved strawberry filling, and milk. Continue to beat until the glaze is smooth and pourable.

Finish the Rolls: Once the rolls are baked, drizzle the glaze generously over the warm rolls. Serve immediately or store in an airtight container for up to 3 days.