On a lightly floured surface, roll the dough into a 14 x 10-inch rectangle. Spread the Strawberry Cream Cheese Filling evenly over the dough. Fold the dough into thirds, like a letter. Cover with plastic wrap, and let rest for 10 minutes.
Butter a 13 x 9-inch baking pan. (I lined my pan with a parchment sling, and then buttered the parchment paper.)
On a lightly floured surface, roll the dough back into a 14 x 10-inch rectangle. Spread the 1/3 cup room temperature butter evenly over the dough, leaving a 1/2-inch border on one long side. Sprinkle the butter evenly with the Strawberry Cardamom Sugar, gently pressing the sugar mixture into the butter.
Starting with one long side, roll the dough into a log, pinching the seam to seal. Trim the ends. With a knife or sharp scissors, slice the log into 12 even pieces. Place the pieces, cut side up, into the prepared pan. Let the buns rise in a warm, draft-free place (75F | 24C) until puffed, about 45 minutes.
While the buns are rising, preheat the oven to 375F (190C).
Bake the buns until golden and puffed, 25-30 minutes. Let cool for a few minutes on a wire rack. Drizzle with Strawberry Cream Cheese Frosting. Serve warm.