Preheat the oven to 375°F. Line a baking sheet with parchment paper.
To make the scones: In food processor, process 1/2 cup of the strawberries with the sugar and half & half or cream until the mixture is smooth. Set it aside.
In a large bowl, whisk together the flour, salt, and baking powder.
Work in the butter, using your fingertips; the mixture should be unevenly crumbly.
In a separate bowl, whisk together the strawberry/cream mixture, the egg, and the vanilla extract.
Add this mixture to the dry ingredients, stirring until the dough just barely starts to come together.
Add the 2/3 cup diced strawberries, gently folding them in; the dough will be quite sticky.
Drop the dough by heaping tablespoonfuls using a cookie scooper onto the prepared baking sheets; each scone should be about the size of a golf ball.
Make the glaze by stirring together the sugar, water, and vanilla until smooth. Drizzle some atop each scone.
Bake the scones until they're just beginning to turn golden brown around the edges, for 18 to 20 minutes.
Serve scones warm. Or allow them to cool completely, and store airtight at room temperature.