Preheat the oven to 350 degrees F. Line a jelly roll pan or baking sheet with edges with parchment paper.
In a medium bowl, add the old fashioned oats and chopped peanuts.
In a medium saucepan, add the peanut butter, butter, and brown sugar. Turn the heat to medium and stir to combine the ingredients.
Once the butter is completely melted and the sugar is no longer grainy, remove from the heat. Add in the vanilla and stir.
Pour the peanut butter mixture over the oats and stir until the oats are completely coated.
In a separate bowl, add the egg white. Whisk the egg white until it is frothy and white. It should take about 1 to 2 minutes of whisking.
Pour the egg white into the peanut butter and oat mixture and stir to incorporate.
Place the granola on the prepared pan and spread out. Make sure the granola isn't layered too thick but can be flattened into large pieces.. This will help bigger chunks to form.
Bake for 10 to 15 minutes and turn the pan around. Do not stir the granola. Stirring the granola will make it break apart.
Bake for an additional 10 to 15 minutes and remove from the oven. Let the granola cool completely. It will come out soft but will harden as it cools.
Break into suitable pieces and store in an airtight container.