In a mixing bowl, combine light brown sugar, ground cinnamon, and instant espresso. Stir until blended.

In a large bowl, whisk together all-purpose flour, instant yeast, and salt. Heat whole milk, granulated sugar, and unsalted butter until melted.

Add the milk mixture to dry ingredients, crack in an egg and mix until a cohesive dough forms. Knead the dough on a floured surface for 5-7 minutes.

Place the kneaded dough into a greased bowl, cover with a towel, and let it rest for 15 minutes.

Roll the rested dough into a rectangle (12x18 inches). Spread softened unsalted butter and sprinkle filling mixture over it.

From the long side, roll the dough tightly into a log, pinch seams to seal, and slice into 9 pieces.

Place the rolls in a greased pan, cover with a towel, and let rise in a warm oven for 30 minutes.

Preheat oven to 350°F; bake rolls for 26-30 minutes until golden brown.

Prepare the coffee glaze while baking by whisking powdered sugar, strong coffee, melted unsalted butter, and vanilla extract.

Drizzle the glaze over warm rolls and let it soak in before serving.