Warm the milk and water to about 110°F/43°C — warm enough to wake the yeast, not scalding.

Sprinkle the yeast over the warm liquid with a pinch of the sugar and let it sit 5–7 minutes until frothy.

In a large bowl, whisk together 3 cups of the flour, the remaining sugar, and salt. Add the melted butter, egg, and the frothy yeast mixture. Stir until a shaggy dough forms.

Turn the dough onto a lightly floured surface. Knead, adding the remaining 1/2 cup flour as needed, until the dough is smooth and elastic — about 6–8 minutes by hand (or 4–5 minutes with a stand mixer).

Lightly oil a bowl, place the dough inside, cover with a towel or plastic wrap, and let it rise in a warm spot until doubled — about 1 to 1 1/2 hours.

In a small saucepan, combine the chopped strawberries, brown sugar, granulated sugar, cinnamon, and lemon juice. Stir to combine.

Mix cornstarch with 1–2 tbsp cold water to make a slurry, then stir it into the strawberry mixture.

Cook over medium heat, stirring frequently, until the mixture thickens and the strawberries release their juices — about 5–7 minutes.

Remove from heat and let cool to room temperature.

Once dough has doubled, punch it down and roll it out on a lightly floured surface to a rectangle about 16×12 inches.

Spread the softened butter evenly over the dough, leaving a small border. Sprinkle the cinnamon evenly, then spoon the cooled strawberry filling across the surface.

Starting from the long edge, roll the dough tightly into a log. Pinch the seam shut and trim about 1/2 inch off each end.

Cut the log into 12 even pieces. Arrange the rolls cut-side up in a greased 9×13-inch pan, leaving space for expansion. Cover and let rise another 30–45 minutes until puffy.

Preheat the oven to 350°F (175°C). Bake the rolls for 22–28 minutes, or until golden brown and set.

While they bake, whisk together cream cheese, powdered sugar, vanilla, and milk to make the glaze.

When the rolls are hot from the oven, drizzle or spread the glaze so it melts into the rolls. Serve warm.