Cut off the hard stem, wash sesame leaves, drain, dry, and roughly chop (tear) them.
Put most of the oil in a food mixer along with chopped (torn) sesame leaves and garlic.
Pulse the food mixer few times before keeping it running to see if you need to add more oil.
Add salt and pepper to taste.
Store it in an airtight jar and fill it up with more olive oil until it comes above the paste. Refrigerate it if you are not using it right away or put it in ice cube maker and freeze it (for easy use).
If you are using mortar and pestle to make this, pound the garlic first, then add pine nuts, and finally the leaves. Mix in oil after the first three ingredients are properly mixed.
Note: I suggest under seasoning the paste if you are going to use it in pasta or if you are adding vegan parmesan to it later on. You can always add more salt/flavoring later depending on how you are going to use it.

A handful of sesame leaves (about 20-30 leaves)
1/3 cup pine nuts, toasted
1/3 cup extra-virgin olive oil
Salt and pepper, to taste
2-3 cloves garlic