If your butter isn't already frozen, put the cup of butter in the freezer for at least 15 minutes while you assemble your ingredients. If possible, have the butter as one whole piece to make grating it easier.
In a large bowl, whisk together the flour, sugar, salt, and baking powder. Grate the frozen butter into the bowl. With a pastry cutter, two forks, or your fingers, mix the butter into the dry ingredients until mixture resembles a coarse meal (pea-sized crumbs of butter will be visible)
Whisk together the cream or buttermilk, egg, and vanilla in a medium bowl. Pour over the dry ingredients and mix gently with a spoon or spatula. Mixture should be slightly dry with some flour still visible. Add the strawberries and basil and gently incorporate. Don't over-mix.
Turn the dough onto a lightly floured surface and bring it together with your hands, pressing the dry spots into the more moistened areas in the dough. The dough should hold together and be slightly sticky. If excessively sticky, sprinkle a little more flour on it, and if excessively dry, add a little cream or buttermilk.
Pat the dough down evenly to about 1 inch thickness. Cut out circle shaped scones using a floured cookie cutter or the rim of a drinking glass. Place scones on a lined baking sheet about 2 inches apart. Brush tops with cream or buttermilk and sprinkle lightly with sugar.
Refrigerate the pan of scones for 15 minutes. Meanwhile, preheat your oven to 400°F. Bake for 22-25 minutes or until scones are golden brown on the edges. Alternatively, freeze the scones completely on the pan, then put them in a sealed bag in your freezer until you're ready to bake. When baking from frozen, add a couple minutes to the baking time. Let cool for a couple minutes on the pan, then remove scones and let cool slightly on wire racks before enjoying. Scones are best eaten warm but will keep 2 or 3 days at room temperature.