In a large mixing bowl, dissolve the yeast and 1 tablespoon of the sugar in warm milk. Let it sit for about 5 minutes, until frothy.
Add the remaining sugar, melted butter, salt, eggs, and gradually mix in the flour until a dough forms. Knead on a lightly floured surface for about 5-7 minutes, until smooth and elastic.
Place the dough in a greased bowl, covering it with a clean cloth. Let it rise in a warm place for about 1 hour or until doubled in size.
Make the Strawberry Filling:
While the dough is rising, combine the chopped strawberries, sugar, cinnamon, and cornstarch in a saucepan over medium heat. Cook for about 5-7 minutes, stirring constantly, until the mixture thickens. Allow it to cool.
Assemble the Rolls:
Once the dough has risen, punch it down and roll it out on a floured surface into a large rectangle, about 1/4 inch thick.
Spread the cooled strawberry mixture evenly over the dough.
Starting with the long side, roll the dough tightly. Cut the log into 12-14 equal pieces.
Place the rolls in a greased baking dish, leaving some space between each for them to expand. Cover and let them rise again for about 30 minutes.
Bake:
Preheat your oven to 350°F (175°C). Bake the rolls for 25-30 minutes, or until golden brown.
Prepare the Glaze:
While the rolls are baking, whisk together powdered sugar, milk (or cream), and vanilla extract in a bowl until smooth.
Finish and Serve:
Once the rolls are done, let them cool for a few minutes before drizzling with the glaze.