• Prepare sweet dough according to recipe.

For the strawberry jam

• Place the strawberries, sugar, salt, and vanilla bean into a medium pan and simmer over medium-low heat for about 30-40 minutes, stirring often, until the strawberries have broken down and the jam has thickened. The jam will cling to a wooden spoon when it is done. Remove from the heat and allow to cool to room temperature. Remove the vanilla bean and discard, then refrigerate the jam until ready to use. (Taste your jam – if it is a little flat, you can add a squeeze or two of lemon juice – about 1/2 teaspoon at a time, until it brightens the flavor.)

To assemble

• Butter ten 3 x 2-inch soufflé molds (see note above about soufflé mold specifics). Line the bottom of each mold with parchment paper, and then generously coat with granulated sugar, tapping out any excess. Place the molds on a baking sheet. Alternatively, you can butter and sugar coat a 9x13 inch pan if you don't have the molds!
• Roll the dough into a 16 x 12-inch rectangle. Brush the entire surface with 2 tablespoons melted butter. Start with 1/2 cup of jam, and spread the jam over the dough. If more jam is needed, add more until there is a thin layer over the dough (you don’t want too much jam, or the next steps will be extra messy). Starting at the long side, roll the dough into a tight cylinder. Pinch the seam gently to seal it and position the dough seam side down. Use a scissors or a sharp knife to cut the dough into 10 equal pieces. Transfer the pieces to the prepared pans and place them cut side up. Cover the pans loosely with plastic wrap and let the dough rise until doubled, 1 to 1 1/2 hours.
• Adjust the oven rack to the middle lower position. Preheat the oven to 350F.
• Remove the plastic and bake 22 to 30 minutes, rotating the pan halfway through, until the rolls are golden brown. While the rolls are baking prepare the icing.
• Transfer the pan to a wire rack and let the rolls cool for a few minutes. Use a kitchen towel or oven mitts to pick up each soufflé mold, then run a knife carefully around the edges of the pan, and flip the roll onto a wire rack. Carefully put the roll right side up, and repeat with the remaining rolls. Let cool for 5 minutes, then place a piece of parchment paper under the wire rack. Pour the icing over each roll. Serve warm.

For the icing

• In a small bowl, mix the cream cheese, butter, milk, salt, and vanilla until smooth. Add 1 cup of the powdered sugar and mix again until smooth. If the mixture is too thin, add more powdered sugar until the desired consistency is reached. Top each bun with a cut strawberry, if desired.