Preheat your oven to 350°F (175°C). Spread the sunflower seeds evenly on a baking sheet. Toast them for about 10-12 minutes, stirring halfway through. Allow the seeds to cool completely before processing. (Optional)
Add the cooled (or raw, if skipping toasting) sunflower seeds to your food processor. Pulse a few times to break them down, then process continuously for about 3-5 minutes until the seeds form a thick paste.
While the processor is running, drizzle in 5 teaspoons of high-oleic sunflower oil, adding more a teaspoon at a time until the desired creamy consistency is reached. Then add honey and sea salt, blending until smooth.
Taste the sunflower butter and adjust sweetness, salt, or texture by adding more honey, salt, or oil as needed. Process again to combine.
Transfer the sunflower butter to a clean glass jar or airtight container. Store at room temperature for short term or refrigerate to extend shelf life.