In a medium saucepan over medium-high heat, combine the diced strawberries, 3 tablespoons brown sugar, lemon juice, and orange zest. Mash the strawberries as they cook to release their juices, about 2-3 minutes. In a small bowl, whisk together the cornstarch and 1 tablespoon water to create a slurry, then stir it into the strawberry mixture. Continue cooking for 2-4 minutes, stirring occasionally, until the mixture thickens and coats the back of a spoon. Remove from heat, reserve 2 tablespoons of the jam for the frosting, then spread the remaining jam on a plate to cool while you prepare the dough.
In a small saucepan, whisk together 2/3 cup water with 1/4 cup plus 1 tablespoon flour over medium heat, stirring constantly for 4-5 minutes until the mixture forms a smooth, thick paste. This technique, called tangzhong, gelatinizes the starch and creates incredibly tender, moist rolls—I always use this method because it keeps the dough from drying out during baking. Remove from heat and let cool for a few minutes while you gather your other dough ingredients.
In the bowl of a stand mixer, combine 3.75 cups flour, 1/3 cup sugar, 2 1/4 teaspoons yeast, and 1 1/4 teaspoons salt. Add the warmed milk (110°F), cream, room-temperature egg (70°F), and 1 teaspoon vanilla extract, then add the cooled flour paste from Step 2. Mix on low speed for 2 minutes until combined. Increase to medium-low speed and add 8 tablespoons softened butter one spoonful at a time, allowing each addition to incorporate before adding more. Knead for 12 minutes total until the dough becomes smooth, elastic, and slightly tacky but not sticky—it should pull away from the bowl sides. I like to do a quick windowpane test by stretching a small piece; if it stretches thin without tearing, the gluten development is perfect.
While the dough rises (you can do this during the first rise if preparing ahead), stir together 1/2 cup room-temperature butter, 3/4 cup brown sugar, and 1 1/2 teaspoons cinnamon in a bowl until well combined. Line a 9x13-inch baking pan with parchment paper. Once the dough has risen to roughly 1.5 times its original size (about 45 minutes), turn it out onto a lightly floured surface and roll it into a 21x15-inch rectangle. Spread the cinnamon-butter mixture evenly over the dough, then spread the cooled strawberry jam from Step 1 over top.
Starting from the long end of the rectangle, roll the dough tightly toward you, creating a long log. Using a sharp knife or dental floss, cut the log into twelve equal pieces (approximately 1 3/4 inches each), then arrange them cut-side up in the prepared 9x13-inch pan, spacing them evenly. Cover loosely with a damp towel or plastic wrap and let rise in a warm place for 1-2 hours until the rolls are puffy, nearly doubled, and they touch each other slightly. About 20 minutes before the rolls finish rising, preheat your oven to 325°F.
Place the pan in the preheated 325°F oven and bake for 30-40 minutes until the rolls are golden brown on top and the centers reach an internal temperature of 185°F (use an instant-read thermometer inserted into the center roll). The lower oven temperature ensures the rolls bake through evenly without over-browning the tops. Remove from the oven and let cool in the pan for 5 minutes—this brief rest prevents the frosting from melting too quickly.
While the rolls cool, prepare the frosting by beating 6 tablespoons butter and 4 ounces softened cream cheese together until fluffy, about 1-2 minutes. Sift in 1 1/4 cups confectioners sugar and beat until smooth. Add the 2 tablespoons reserved strawberry jam from Step 1 and 1 1/2 tablespoons heavy cream, beating until the frosting is spreadable but not runny. Spread the frosting generously over the warm rolls while they're still slightly warm—the warmth helps it set beautifully. Serve immediately or at room temperature.