Preheat the oven to 400 degrees F.
Line an 18x26-inch baking sheet with parchment paper.
In a large bowl, add 2 cups of the flour, the granulated sugar, the baking powder, and the salt and whisk to combine.
Add the cold butter to the flour mixture and, using a pastry blender or by hand, quickly cut the cold butter into the flour mixture until the mixture resembles coarse meal, with a few large butter lumps.
In a small bowl, add 1 cup of the heavy cream and 1 teaspoon of the vanilla extract and whisk to combine.
Add the heavy cream-vanilla mixture to the flour mixture and, with a spatula, stir until the dough begins to form. Be careful not to overmix.
Add the strawberries to the dough mixture and gently fold to combine.
Using the extra flour, lightly dust a work surface.
Turn the dough out onto the prepared work surface and gently knead it just until a ball forms.
By hand, form the dough into a 1-inch-thick circle by patting and gently pressing the dough. Be careful not to overwork the dough.
With a sharp knife, evenly cut the dough into 8 triangles.
In a single layer, place the dough triangles on the prepared baking sheet.
Transfer the baking sheet to the freezer and let them chill to prevent the scones from spreading while baking, about 15-20 minutes.
Transfer the scones from the freezer and, with a pastry brush, brush the tops of the scones with the remaining heavy cream.
Evenly sprinkle the turbinado sugar on top of the scones.
Bake until the scones are golden-brown on the bottom and around the edges, about 18-23 minutes.
Transfer the baking sheet from the oven to a wire rack and let the scones cool on the baking sheet for 5 minutes.
Transfer the scones directly to the wire rack and let them cool completely.
While the scones are cooling, in a small bowl, add the confectioners' sugar, the milk, and the remaining vanilla extract and whisk until smooth.
Generously and evenly drizzle the glaze over the cooled scones.
Serve.