Step 1: Prepare the Strawberry Filling

1. In a medium saucepan, combine strawberries, sugar, cornstarch, lemon juice, lemon zest, and salt.
2. Heat over medium heat, stirring frequently until the mixture comes to a simmer.
3. Continue cooking for 5-10 minutes until the mixture thickens to a jam-like consistency.
4. Remove from heat and allow to cool completely. Refrigerate to speed up the cooling process.

Step 2: Make the Dough

1. In a large mixing bowl, combine 2 cups of flour, sugar, salt, and yeast.
2. Add warm milk, melted butter, eggs, and vanilla extract to the dry ingredients.
3. Beat with an electric mixer on low speed until combined, then switch to medium speed and beat for 3 minutes.
4. Gradually stir in the remaining flour to form a soft, slightly sticky dough.
5. Turn the dough onto a floured surface and knead for 6-8 minutes until smooth and elastic.
6. Place in a greased bowl, cover with a damp towel, and let rise in a warm place for about 1 hour or until doubled in size.

Step 3: Assemble the Rolls

1. Punch down the risen dough and turn onto a lightly floured surface.
2. Roll the dough into a large rectangle, approximately 18×12 inches.
3. In a small bowl, mix the softened butter, brown sugar, and cinnamon to create a light cinnamon mixture.
4. Spread the cinnamon mixture over the dough, leaving a 1/2-inch border around the edges.
5. Carefully spread the cooled strawberry filling over the cinnamon layer.
6. Starting from the long side, tightly roll up the dough into a log.
7. Using a sharp knife or dental floss, cut the log into 12 equal slices.

Step 4: Second Rise and Baking

1. Place the rolls in a greased 9×13-inch baking dish, spacing them evenly.
2. Cover and let rise in a warm place for 30-45 minutes, or until nearly doubled in size.
3. Preheat oven to 350°F (175°C).
4. Bake for 25-30 minutes, or until the rolls are golden brown.
5. If the tops are browning too quickly, cover loosely with aluminum foil.

Step 5: Prepare the Cream Cheese Frosting

1. In a medium bowl, beat cream cheese and butter until smooth and creamy.
2. Gradually add powdered sugar, beating well after each addition.
3. Mix in vanilla extract and enough heavy cream to reach your desired consistency.
4. For a strawberry-flavored frosting, stir in 1-2 tablespoons of strawberry jam.

Step 6: Finish and Serve

1. While the rolls are still warm (but not hot), spread the cream cheese frosting generously over the top.
2. The heat will help the frosting melt slightly into the rolls for extra gooeyness.
3. Serve warm and enjoy!