Add the basil, cilantro, Parma, walnuts and garlic to a food processor and pulse just until combined. Add lemon juice and za'atar and pulse to combine. Then drizzle in olive oil until a paste forms. You can store this in the refrigerator for up to a week.
Now, grilled cheese time! Slice your bagel in half and schmear mayonnaise on the inside.
Heat a large pan over medium-low heat and add one half of the bagel, mayo side down. Then carefully top with cheese, and spoon on pesto, avoiding the hole. Top with the other bagel half, gently pushing down, cover with a top, and cook for 3-4 minutes until the cheese starts to melt and the bottom is nice and brown.
Carefully flip with a spatula and cook for another 3-4 minutes until cheese is melty and bubbly and you can't wait anymore you must eat the grilled cheese!