For the croutons:
Preheat the oven to 375° F. Line a rimmed baking sheet with parchment paper or foil.
Heat a large skillet over medium heat. Add 3 tbsp of olive oil, and turn the pan three times.
Melt the butter into the oil. When it foams, add 2 cloves of crushed garlic and 1 tsp of black pepper. Stir for about 1 minute.
Add the cubed bread and toss to coat.
Transfer the croutons to the baking sheet. Sprinkle 1/2 cup of each cheese over the bread and bake for 20 to 25, until deeply golden.
Add the Za'atar and toss while warm. Let cool. Croutons will stay fresh in an airtight container for 7 to 10 days.
For the dressing:
Place the tahini in the bowl of a food processor along with the remaining garlic, lemon juice, pepper, mustard, and Worcestershire (if using).
Turn the processor on and stream in 1/3 cup of water to thin the paste.
Stream in remaining olive oil to form the dressing (it should be thick, but pourable).
Add remaining cheese and pulse a few times to combine all ingredients.
Make the salad:
Pile 10 to 12 cups of combined greens in a large bowl.
Toss with enough dressing to coat generously. Top with croutons and serve.