In the bowl of a stand mixer, beat Butter (1 cup) with the paddle attachment to make it creamy and fluffy.
Add Parmesan Cheese (2/3 cup), Fresh Basil (1/3 cup), Salt (1 pinch), and Olive Oil (2 tablespoon). Let them get completely mixed in.
Turn the mixer speed to low and slowly add in the All-Purpose Flour (2 cup) just until it disappears and a dough forms. It's important not to overwork it.
Turn the dough out onto a large piece of plastic wrap. Form it into a long, round log by wrapping it firmly in the plastic and gently rolling it to make it nice and round. Allow the log of dough to chill in the refrigerator for at least 3 hours or up to overnight.
When the dough has chilled, preheat the oven to 325 degrees F (160 degrees C) and line two sheet trays with silicone mats or parchment paper.
Take the dough out and slice it into about 1/2 inch slices to turn it into pretty little crackers. Spread them out evenly on the sheets. There should be a yield of about 35-40 crackers.
Bake the crackers for about 20 minutes. They should just start to get golden around the edges. Take them out and let them cool. Then just seal them in airtight containers until you are ready to serve them! They will keep for a couple of days and can be made ahead.