In a bowl, combine warm milk and sugar. Sprinkle yeast over the mixture and let it sit for about 5 minutes, or until frothy. Add melted butter, vanilla extract, and salt to the yeast mixture. Stir in the egg. Gradually add flour, one cup at a time, until a soft dough forms.
Knead the dough on a floured surface until smooth and elastic.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1 hour or until doubled in size.
In a small saucepan, combine mixed berries, sugar, and cornstarch. Cook over medium heat until the berries release their juices and the mixture thickens.
Remove from heat and let it cool.
Preheat the oven to 375°F (190°C).
Roll out the dough on a floured surface into a rectangle. Spread the cooled berry filling evenly over the dough. Roll the dough tightly from the long side, forming a log. Slice into 12 equal rolls.
Place the rolls in a greased baking dish. Bake for 20-25 minutes or until the rolls are golden brown.
In a bowl, whisk together powdered sugar, milk, and vanilla extract until smooth. Drizzle the glaze over the warm rolls before serving.