To the bowl of a stand-mixer fitted with the dough hook attachment, add the yeast, sugar, and milk. Mix together and allow to stand 5 minutes until foamy. Add the egg and butter and mix until combined. Incorporate the flour and salt until a soft dough forms and pulls away from the sides of the bowl. If too sticky, add more flour by the tablespoon until it comes together. Turn the mixer on medium-high and knead dough 5 minutes. Cover the bowl and allow to rise in a warm place until doubled, about 1 hour.
When the dough is done rising, put a small saucepan over medium heat. Add the brown sugar, espresso, and cinnamon. Stir until the sugar dissolves and the mixture becomes a glossy syrup 2-4 minutes. Remove from heat and set aside.
Turn the dough out onto a floured work surface and roll into a large rectangle. Using your fingers, spread the top of the dough with the soft butter. Sprinkle chocolate chips over the butter. Drizzle the espresso syrup over the top. Roll the dough up, trim off the edges with a sharp knife, and slice into 2-inch-wide rolls. Place rolls into a round baking dish or pie plate, allowing room for them to rise. Cover loosely with foil and allow them to rise another 45 minutes.
Preheat oven to 400. Bake the rolls with the foil for 20 minutes. Remove foil and bake another 10 minutes, or until golden brown on top and cooked through.
In the last 10 minutes of baking, whisk together the powdered sugar, cinnamon, vanilla, and maple syrup. Gradually incorporate espresso until a smooth, runny glaze forms. When rolls are done, pour the glaze over top while hot. Best eaten fresh out of the oven.