Toss butter and flour together in a mixing bowl, squishing it with your hands to create a fine crumble. You can also use a pastry cutter.
When butter is coated in flour and pea-size, add in sugar, baking powder, and salt. Stir.
Add in candied pineapple, coconut, and basil, mixing with your hands until homogenous.
In a separate bowl whisk together sour cream, milk, egg, lime zest, and extracts. Pour over the flour mixture and stir with a spoon until just combined. Batter should be sticky but thick enough to hold its shape.
Line two baking sheets with parchment paper. Using a 1/4 cup measuring cup or ice cream scoop, drop scone batter onto the pan, 7 per pan.
Place the scone-lined pans in the refrigerator to chill for 15 minutes. While they chill, preheat the oven to 400°F.
Bake the sheets one at a time, for 20-22 minutes, rotating half way through baking.
While they are baking, prepare the glaze. Allow the scones to cool completely before glazing them.