In a stand mixer bowl, mix the flour, sugar, yeast, and salt. Add the cream, milk, egg, vanilla, and tangzhong to the bowl. Knead on low speed with the dough hook for 2 minutes until it forms a rough dough ball.
With the mixer running on low, add the softened butter one tablespoon at a time, letting it fully incorporate before adding more. Continue kneading for another 8-10 minutes or until the dough looks smooth and elastic.
Remove the dough from the bowl and pull the sides into the bottom to create a smooth round ball. Place it seam-side down back into the mixing bowl. Cover with plastic wrap and set aside to rest for 30 minutes.
While the dough rests, make the filling. In a large bowl, combine the butter, brown sugar, and cinnamon until smooth. Set aside.
Place the rested dough on a lightly floured surface. Roll it out into a 15×21 rectangle, with the longest side closest to you. Dollop the cinnamon sugar filling across the surface of the dough, then spread it across, leaving a ½-inch border clean at the top. Then spread all but 1-2 tablespoons of the strawberry jam on top. The reserved jam will be used in the frosting!
Use a pizza cutter to cut twelve 1 ¾-inch strips. Roll each strip away from you, then carefully transfer them to a parchment-lined 9×13 baking pan.
Cover the pan with plastic wrap and set it aside to rise for 1-2 hours, or until the rolls have doubled in size. Meanwhile, preheat the oven to 325°F/162°C.
Bake for 30-40 minutes or until the internal temperature of the center rolls reaches 185°F. Let them cool on a wire rack while you make the frosting.
In a medium bowl, combine the butter, cream cheese, and powdered sugar until smooth. Whisk in the milk, reserved strawberry jam, and strawberry extract. Spread over the sweet rolls and enjoy!