In the bowl of a stand mixer (or a large bowl), combine the warm milk, granulated sugar, and yeast. Let it sit for 5-10 minutes until foamy, indicating the yeast is active.

Stir in the cooled brewed coffee, melted butter, and egg. Mix until well combined.

Gradually add 3 cups of the all-purpose flour and the salt. Using the dough hook attachment (or a wooden spoon), mix on low speed until a shaggy dough forms. Add the remaining ½ cup of flour, a little at a time, until the dough comes together and pulls away from the sides of the bowl. The dough should be soft and slightly sticky.

Increase speed to medium-low and knead for 5-7 minutes, until the dough is smooth and elastic. If kneading by hand, turn the dough out onto a lightly floured surface and knead for 8-10 minutes.

Lightly grease a large clean bowl with oil. Place the dough in the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 to 1.5 hours, or until doubled in size.

While the dough rises, prepare the filling: In a small bowl, combine the softened butter, brown sugar, ground cinnamon, and instant espresso powder. Mix until well combined and spreadable.

Lightly grease a 9x13 inch baking dish.

Once the dough has doubled, gently punch it down. Turn the dough out onto a lightly floured surface and roll it into a large rectangle, approximately 12x18 inches.

Evenly spread the coffee-cinnamon filling over the entire surface of the dough, leaving a small border (about ½ inch) on one of the long edges.

Starting from the opposite long edge, tightly roll the dough into a log. Pinch the seam to seal it.

Using a sharp knife or unflavored dental floss, cut the log into 12 equal slices (about 1.5 inches thick). Place the cut rolls into the prepared baking dish, leaving a little space between them.

Cover the baking dish loosely with plastic wrap or a clean kitchen towel and let the rolls rise again in a warm place for 30-45 minutes, or until puffy and almost doubled.

Preheat your oven to 375°F (190°C) during the last 15 minutes of the second rise.

Bake for 25-30 minutes, or until the rolls are golden brown and cooked through. If the tops brown too quickly, you can lightly tent them with aluminum foil.

Remove from the oven and let cool slightly while you prepare the frosting.

In a medium bowl, beat the softened cream cheese and butter with an electric mixer until smooth and creamy.

Gradually add the powdered sugar, mixing on low speed until incorporated, then increase to medium and beat until fluffy. Add the cooled brewed coffee, vanilla extract, and a pinch of salt. Beat until smooth and spreadable, adding a tiny bit more powdered sugar if too thin, or a few drops more coffee if too thick.

Spread the coffee cream cheese frosting generously over the warm (but not hot) cinnamon rolls. Serve immediately and enjoy!