Mix together hot water and instant coffee to make a concentrated coffee mix. Add to warm milk. Add yeast and set aside for 5 minutes. The milk and coffee mixture should feel comfortably warm to the touch, but not hot, otherwise it will kill your yeast.
Combine flour, sugar, salt, egg, milk and coffee mixture, and 1/2 cup of tangzhong starter in a medium mixing bowl. Using a stand mixer fitted with a dough hook attachment, mix on medium-low speed until dough comes together. Slowly add pieces of butter until fully incorporated, which could take up to 10 minutes. Continue to mix in stand mixer for ~10 - 15 minutes on medium-low speed until a smooth, elastic dough forms. Every few minutes, pause and do the window pane test to see if the gluten has developed. To make the dough by hand, please see notes above.
Lightly grease mixing bowl and place dough in bowl. Cover with plastic wrap and let rise for 40 - 60 minutes until roughly doubled in size.
Mix together brown sugar and cinnamon and lightly grease your round baking tin. Generously flour your countertop. Remove the dough from the bowl and place on the countertop. Flour the surface of the dough and your rolling pin. Roll the dough out into a 15in. by 10in. rectangle. Evenly sprinkle the surface with brown sugar and cinnamon mixture, making sure to spread all the way to the edges of the rectangle. With the long side of the rectangle facing you, roll into a 15in. cylinder. Cut into 8 equal slices and place in your baking tin.
Preheat oven to 350°F. Allow the rolls to proof for 45 - 60 minutes. When you press your finger into the rolls, the dough should slowly come back about halfway.
Place in the lower third of the oven and bake for 20 - 25 minutes until it makes a hollow sound when tapped.