Preheat the oven to 350ºF. Line an 8×8-inch baking dish with parchment paper.
In a small pot over very low heat, combine the chocolate, honey, and sunflower seed butter. Stir constantly until melted and smooth. Transfer to a food processor fitted with the steel blade. Scoop the avocado flesh into the food processor and add the remaining ingredients. Process until creamy and very smooth, about 1 minute. Transfer the batter to the parchment-lined pan and spread it out evenly.
Bake for 25-30 minutes until a toothpick inserted comes out mostly clean or with a few moist crumbs attached. Cool completely, then refrigerate for 2 hours before cutting into 16 squares. Store brownies in the refrigerator or freezer in an airtight container.