In a stand mixing bowl, mix together the all-purpose sugar, yeast, and salt until combined.
Add the egg, milk, vanilla, and tangzhong to the bowl. Knead on low speed with the dough hook for 2 minutes until it starts to form a shaggy dough ball.
With the mixer running on low, add the softened butter ½ tablespoon at a time, letting it fully incorporate into the dough before adding more.
Once all the butter is added, continue kneading the dough for another 8-10 minutes or until the dough looks smooth and elastic. The dough should be sticking to the bottom of the bowl. If it seems too wet and is sticking to the sides of the bowl, add flour one tablespoon at a time. If the dough seems dry, add half a tablespoon of milk at a time. With lightly buttered hands, remove the dough from the bowl and pull the sides down into the bottom center, to create a smooth round ball.
Place the dough seam side down into a large lightly buttered bowl. Cover with plastic wrap and let it rise in a warm spot for about 45-60 minutes, or until doubled in size.
Roll the dough out on a lightly floured surface into a 14x18 rectangle, with the long (18-inch) side closest to you.
Use an offset spatula to spread the strawberry jam in an even layer all the way to the edges.
Then use a pizza cutter to cut 12, 1 ½ inch strips. Roll each strip away from you, then carefully transfer them to a parchment-lined 9x13 baking tray.
Cover the pan with plastic wrap and set it aside to rise for another 45-60 minutes, or until the rolls double in size. Meanwhile, preaheat the oven to 325 F/162 C.
Bake the rolls for 23-26 minutes, or until the tops are lightly golden brown. Let the pan cool on a wire cooling rack while you make the glaze.
In a medium bowl, combine the butter, cream cheese, and powdered sugar until smooth. Then whisk in the milk and reserved strawberry jam. Spread over the cinnamon rolls and enjoy!