Allow the tea to infuse in the milk using a tea strainer for 15 minutes until the milk has cooled down to lukewarm. Remove and discard the jasmine tea leaves, and stir the yeast into the lukewarm milk. Allow the mixture to rest for 5 minutes.

In the bowl of an electric mixer fitted with a paddle attachment, mix together the eggs, flour, butter, sugars, salt, rosemary, and milk mixture until a rough dough forms. Knead the dough by hand or with the dough hook attachment of your stand mixer until smooth. Place the dough in a clean and lightly-greased bowl. Cover it and allow to rise out of direct sunlight until doubled in size, about 1 hour.

Roll out the dough into a rectangle until the dough is about 1/2 inch thick. Spread the softened butter across the top of the dough, and then sprinkle the brown sugar and fresh rosemary filling over it. Roll up the dough like a jelly roll, and then use a sharp knife to cut it into roughly 2-inch thick slices. Place the rolls, twist side up, in a greased large Dutch oven or casserole pan. Once the pan is full, cover and allow to rise out of direct sunlight until the rolls are puffy and touching each other in the pan, about 1 hour.

Preheat the oven to 400 degrees Fahrenheit. Remove the cover and bake the rolls until golden on top, about 15-20 minutes.

While they're baking, whisk together the glaze ingredients in a small bowl until completely smooth. Set aside.

Once the rolls are done, allow them to cool for 15 minutes before drizzling the glaze over the top of them and serving. Serve any leftover glaze alongside the rolls for dipping.