Prepare Strawberry Filling: In a medium saucepan, combine fresh or frozen strawberries, sugar, and lemon juice. Cook over medium heat, stirring occasionally, for about 10 minutes until thickened and bubbling. Remove from heat and blend the mixture until smooth. Allow the strawberry filling to cool completely in the refrigerator while you prepare the brioche dough.

Make Brioche Dough: In a large mixing bowl, combine all-purpose flour, sugar, salt, and instant dry yeast. Add the warm milk, softened unsalted butter, and the room-temperature egg. Using a stand mixer with a dough hook, knead the mixture for 5 to 7 minutes, until the dough is smooth and elastic. Cover the bowl with a towel and let it rise in a warm, draft-free area for about 2 hours, or until doubled in size.

Shape the Rolls: Once the brioche dough has risen, punch it down and turn it out onto a floured surface. Roll the dough into a large rectangle, approximately 12x18 inches. Spread the cooled strawberry filling evenly over the dough, leaving a small border around the edges. Starting from one long side, roll the dough tightly into a log and cut it into 12 equal pieces, placing the rolls cut-side up in a greased baking dish.

Second Rise: Cover the baking dish with a clean kitchen towel and let the rolls rise until puffy, about 30 to 60 minutes. Meanwhile, preheat your oven to 350°F (180°C). The rolls should be nearly doubled in size, fluffy to the touch, and ready to go into the oven for baking.

Bake: Once preheated, place the baking dish in the oven and bake the rolls for 20 to 25 minutes. Look for a golden-brown color on top and a soft, slightly springy texture when lightly pressed. Once baked, remove them from the oven and let cool for about 10 minutes while you prepare the glaze.

Prepare Glaze: In a mixing bowl, combine softened cream cheese, softened butter, confectioners' sugar, and vanilla extract. Use a hand mixer to beat the mixture until smooth and creamy. Gradually add in the cold strawberry puree until thoroughly blended. The glaze should be velvety and thick enough to spread over the warm strawberry cinnamon rolls.

Garnish: Generously drizzle or spread the tangy cream cheese glaze over the warm strawberry cinnamon rolls. Serve these delightful strawberry cinnamon rolls immediately.