Preheat the oven to 300 degrees F and line a baking sheet with parchment paper.
Add the peanuts and sea salt to a food processor. Blend until the mixture becomes smooth and creamy, scraping down the sides as needed.
Slowly drizzle in the olive oil while blending until the peanut butter reaches your preferred consistency. Transfer to a large bowl.
In a separate bowl, combine the ground oats, white sugar, brown sugar, salt, vanilla, and olive oil until evenly mixed and crumbly.
Spread the streusel mixture evenly onto the prepared baking sheet.
Bake for 20-30 minutes , until golden brown and fragrant.
Allow the streusel to cool completely. Break it into clusters of your preferred size.
Fold the cooled streusel clusters into the creamy peanut butter until evenly distributed.
Transfer the spread to an airtight jar and store at room temperature for up to one week or refrigerate for longer storage. Stir before serving if natural oil separation occurs.