Add the butter from the dough ingredients and the filling ingredients ( ¾ cup or 1 and ½ sticks) to a small saucepan and melt. Once melted, stir constantly with a heat safe spoon until the butter turns brown and smells toasty like caramel. Pour into a heat safe bowl and set aside to cool off.
Add the sugar and yeast to a large bowl. Add the milk and stir. Let the yeast activate for about 5-10 minutes or until bubbly and foamy. Add the eggs, honey. Measure out ¼ cup of the browned butter and add to the yeast mixture. Add 3 and ½ cups of the flour and the salt. Stir with a wooden spoon until everything comes together. Use your hands or the kneading attachment on a stand mixer to knead the dough very well.
If the dough is sticking to your hands, add more flour 1 tablespoon at a time until the dough is no longer sticky. It should be slightly tacky, but easy to work with and not sticking to your hands. Cover the bowl with a towel and let the dough rise in a warm place for 1 hour.
While the dough is rising, make the filling. Mix together the remaining browned butter, the brown sugar and cinnamon in a small bowl. Flour your work surface and roll out the dough into a rectangle large enough to get 12 cinnamon rolls. This doesn't need to be perfect, just eyeball it. Spread the filling over the dough, leaving about ½ an inch around all sides without filling.
Roll the dough up lengthwise into a log. Pinch the ends together to seal. Use a large knife or floss to cut the log into 12 pieces. Place each roll into a 9x13 pan lined with parchment paper (4 rows of 3 cinnamon rolls). Cover the rolls with a towel and let rise for another 45 minutes - 1 hour or until the cinnamon rolls have almost doubled in size.
Pour the heavy cream over the rolls and bake at 350 ℉ for 23-25 minutes or until lightly golden brown. While the cinnamon rolls are baking, make the icing. Beat the cream cheese, butter and vanilla in a medium mixing bowl until light and fluffy. Add the espresso powder and beat again. Add the powdered sugar and beat until smooth.
Spread the icing over the hot cinnamon rolls and serve. Store in an airtight container at room temperature for up to 5 days. Best served warmed.