In a mixing bowl, combine the flour, sugar, baking powder, and salt. Stir or whisk until everything is evenly distributed.
Add the chilled butter pieces and cut them into the dry ingredients using a pastry blender or your fingers. Continue until the mixture looks sandy with a few larger butter pieces scattered throughout. Keeping the butter cold is important for flaky scones.
Fold the chopped strawberries into the flour mixture, coating them lightly to help prevent excess moisture.
In a separate bowl or measuring cup, whisk together the eggs, half-and-half, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and gently stir with a spatula until a soft dough forms. The dough should look slightly uneven and crumbly in places. Avoid overworking it.
Transfer the dough to a lightly floured work surface. Bring it together with your hands and divide it into two equal portions.
Shape each portion into a round about 1 inch thick. Using a sharp knife or bench scraper, cut each round into 6 wedges.
Arrange the wedges on a parchment-lined baking sheet. Place the tray in the freezer for about 20 minutes to chill the dough and solidify the butter before baking.
Meanwhile, preheat the oven to 375°F.
Bake the scones for 16–18 minutes, or until lightly golden on top and baked through.
To make the glaze, whisk together the powdered sugar, half-and-half, and vanilla until smooth and pourable. Once the scones have cooled, drizzle the icing over the tops and allow it to set before serving.