Scones: Whisk together the baking mix and sugar in a large bowl. Mix in the butter with your hands or a pastry blender until the butter is the size of peas. Beat the eggs well with the 1/4 cup milk in a small bowl. Pour the wet ingredients into the dry ingredients and combine until just blended. Do not over mix. Gently fold in the blueberries. Turn the dough out onto a floured surface and pat into a 3/4-inch thick square. Cut into 4 squares, then cut each square into 2 triangles. Arrange the scones on an ungreased baking sheet and bake until golden brown, about 15 minutes. Remove to a wire rack and let cool a bit before glazing.
For the glaze: Whisk together the confectioners' sugar, lemon juice, and vanilla until smooth. Pour evenly over the warm scones. Transfer to a serving platter and serve.