In a mixing bowl, whisk together the flour, granulated sugar, salt, and baking powder. Add the butter in cubes and rub them into the mixture until it resembles coarse crumbs. Let the mixture chill in the refrigerator.
In a separate mixing bowl, whisk together the buttermilk, egg, and vanilla extract. Pour the milk mixture into the flour mixture and gently mix until a dough forms. Stir in the cream cheese and strawberries.
Place the dough on a generously floured surface. Press the dough down and divide it into three parts. Stack the three parts on top of each other and press down to create layers. Let the dough chill in the refrigerator if it becomes too sticky.
Place the dough on a floured surface and press it down into a circle. Slice each circle into 8 wedges.
Line a baking sheet with parchment paper. Place the scones on the baking sheet at least 2 inches apart.
Let the scones chill in the refrigerator for at least 30 minutes. Preheat the oven to 400º F.
Brush the scones with buttermilk and sprinkle turbinado sugar on top.
Bake the scones for 18-24 minutes or until they are golden brown on top. Remove the scones from the oven and let them cool.
In a mixing bowl, whisk together the powdered sugar, milk, and vanilla extract. Use a fork or other utensil to drizzle the glaze on top of the cooled scones.
Serve the scones warm or at room temperature.