Baking – How do packaged cookies stay good for so long

Three things:

-You can flavor the sugar by mixing aromatic herbs into it and leaving it sit for a week or two. Rosemary pairs well with sweet desserts, as would lavender or basil. Sift out the herbs once you're ready to use the sugar.

-You can try replacing the butter in this recipe (or half of it) with some very good olive oil, as in this recipe from the NYT:

http://dinersjournal.blogs.nytimes.com/2008/03/07/recipe-of-the-day-olive-oil-cookies-with-red-wine-and-rosemary/

That recipe isn't for shortbread cookies, but the technique may still be valid. No guarantees that it will give you the texture you want, but great olive oil has all of the grassy and fruity characteristics that you're after.

-I'm not terribly familiar with matcha, but couldn't you just take some regular green tea leaves and powderize them in a spice grinder?

If you take the pecans out of pecan sandies, what you have left I believe is basically a short bread cookie, although those are traditionally presented in wedges.

Starting by searching for shortbread cookie recipe will give you a much better starting point.

These recipes tend to have a basis as simple as you list, although some embellish by dipping in chocolate and so on. Others substitute cornstarch for some of the flour, to help promote the frangible, delicate texture (cornstarch has no gluten precursors like flour, so it doesn't bring risk of creating a tough or rubbery cookie).

The recipes you are reading which contain baking powder probably (without reading the recipe, its difficult to say for sure) use it to... well... literally create a small amount of leavening, or airiness in the cookie. This will contribute to its crumbly texture, especially if some toughness from overworking the flour is present. As you have noted, it is not necessary in this type of recipe.

Side note: cream of tartar is an acid, not a leavening agent.