Add the chopped strawberries, jalapeño pepper slices, and sugar to a medium bowl. Stir to combine.
Cover the bowl and let it sit at room temperature for 1 hour.
Pour all the contents of the bowl, including any accumulated juices, into your blender and process until smooth.
Transfer the purée to a re-sealable container and refrigerate it until you're ready to use it. The purée can be prepared ahead of time and stored in your refrigerator for 2-3 days.