Prepare the Strawberry Filling: In a medium saucepan over medium heat, combine the strawberries, brown sugar, and lemon juice. Cook until the strawberries break down and release their juices (about 5-7 minutes). In a small bowl, mix the cornstarch and water to create a slurry. Add this to the strawberry mixture and cook, stirring, until thickened. Set aside to cool completely.

Make the Tangzhong: In a small saucepan, whisk together the flour and water over medium heat. Cook, stirring constantly, until the mixture thickens into a paste. Remove from heat and let it cool to room temperature.

Prepare the Dough: In a large mixing bowl, combine the flour, sugar, yeast, and salt. Add the milk, egg, vanilla extract, and cooled Tangzhong. Mix until a shaggy dough forms. Add the softened butter and knead until the dough is smooth and elastic (about 8-10 minutes by hand or 5-7 minutes with a stand mixer). Place the dough in a lightly greased bowl, cover, and let it rise in a warm place for 1-1.5 hours, or until doubled in size.

Assemble the Rolls: Punch down the dough and roll it out on a lightly floured surface into a rectangle about 12x18 inches. Spread the cooled strawberry filling evenly over the dough. Starting at one long edge, roll the dough tightly into a log. Slice the log into 12 equal rolls. Arrange the rolls in a greased 9x13-inch baking dish, cover, and let rise for 30-45 minutes, until puffy.

Bake: Preheat your oven to 350°F (175°C). Bake the rolls for 20-25 minutes, or until golden brown.

Prepare the Glaze: Beat the cream cheese and butter until smooth. Add powdered sugar, reserved strawberry filling, and milk. Mix until smooth and spreadable. Spread the glaze over the warm rolls.