• Preheat oven to 400°.
• Line 2 rimmed baking sheets with parchment paper. Set aside.
• In a large bowl, combine flour and sugar, whisking well. Using a pastry blender, cut butter into flour mixture until mixture resembles coarse crumbs. Add basil and lime zest, stirring to incorporate. Set aside.
• In a measuring cup, combine coconut milk and coconut extract, whisking to blend. Add milk mixture to flour mixture, stirring until a dough forms. Bring mixture together with hands until a stiff dough forms. (If mixture seems dry, add more coconut milk, 1 tablespoon at a time, until uniformly moist.)
• Turn dough out onto a lightly floured surface. Knead gently 3 to 4 times. Using a rolling pin, roll dough to ½-inch thickness. Using a 2½-inch round cutter, cut rounds from dough. Place scones 2 inches apart on prepared baking sheets.
• Bake until edges of scones are golden brown and a wooden pick inserted in the centers comes out clean, approximately 11 minutes.