In a small saucepan, add strawberries, sugar, and water. Turn heat to medium high and bring to a boil. After a few minutes, mash the berries a bit with a rubber spatula, spoon, or potato masher.
Place a wire mesh strainer over a medium measuring cup that holds at least 2 cups. Pour strawberry syrup through wire mesh strainer and, using the back of a spatula, gently press all of the juice out of the strawberries, leaving the seeds and basil behind.