I make the Chicken Shawarma recipe all the time, too, and haven't had this problem. For me, it's critical to read the comments/notes before I try the recipe, sometimes there is a critical comment that vastly improves the recipe (it will be the top one under "most helpful" with the most likes).
Other recipes I cook on repeat:
Lemony Orzo with Asparagus and Garlic
Braised White Beans and Greens
Sticky Miso Salmon Bowl
Roasted Chicken Thighs with Cauliflower
Crispy Gnocchi with Brussel Sprouts
Sauteed Chicken with Meyer Lemon
Salmon and Tomatoes in Foil
There is also a reddit group for NYT cooking that comments on recipes and offers advice on what may have gone wrong.
https://www.reddit.com/r/NYTCooking/
Good luck!