Preheat oven to 400F. Line baking sheet with parchment paper.
In a large mixing bowl, whisk together flour, baking powder, baking soda, salt and sugar. Add butter and work it into the mixture with two forks or a pastry cutter until the mixture resembles coarse meal.
Add egg, milk, and heavy cream into the mixture and mix until just moistened. Fold in strawberries with a spatula.
Turn dough over onto a floured surface and shape into a round 8 inch ball. Cut the dough into 8 triangles, and place on the baking sheet. Bake for 18 to 25 minutes or until golden brown.
Meanwhile, prepare glaze by whisking together heavy cream, confectioners' sugar, and vanilla in a small bowl until smooth. Drizzle over cooled scones and serve when the glaze is set.