Fill a medium bowl with ice and water and set next to the stovetop.
Fill a medium saucepan with water and bring to a boil. Add the basil leaves. Once they have just wilted, about 5 to 10 seconds, use a slotted spoon or skimmer to transfer the basil leaves to the ice water. Once cool, place the leaves in a folded kitchen towel or a few paper towels and squeeze out as much liquid as possible.
Place the basil leaves in a blender and add ½ cup of the grapeseed oil. Blend until roughly chopped, then, with the blender running, add the remaining grapeseed and olive oil and purée until completely smooth.
Strain into an airtight container and refrigerate for up to one week.