Preheat oven to 375 degrees. Line a baking sheet with parchment paper.
SCONES: In a large mixing bowl, combine flour, sugar, baking powder, and salt. Cut butter and shortening into dry ingredients, using a pastry blender or fork until it resembles coarse corn meal.
In a separate bowl, combine cream with beaten egg, add to dry ingredients. Mix just until combined. Gently toss in frozen blackberries.
Knead dough 5-6 times on a generously floured surface, folding dough in half on top of itself each time. Roll the dough into a dome, with center slightly higher than the outside edge. Cut in half, then cut each half into quarters.
Place scones on a prepared baking sheet. Bake for 15-17 minutes or until lightly brown
LEMON GLAZE: In a medium bowl, beat all ingredients together until smooth, adding milk a teaspoon at a time until you've reached desired consistency. Drizzle over warm scones.