Just Bento

If you use whole wheat pastry flour for baked goods it does not make them flat or tough at all. I use it in all my baking now and no one can tell the difference. Just make sure not to over mix because that can make things tough or flat.

Shortbread is so rich I'm not sure that either sesame or matcha would work well with it. It's for the same reasons why iced shortcake (with a frosting) is not commonly available. Shortcake with yuzu peel baked into it... that's a combination I can imagine (shortcake with grated lemon zest mixed into the butter, flour and sugar is delicious).

Here's a recipe I use for a lighter crisper kind of cookie. It's not that different to shortbread, but I've added sesame seeds (crushed and whole). You could omit the sesame and add a matcha icing, which should work.

Ingredients
150grams Flour
1gram Baking powder
20grams crushed sesame (browned on a hot pan then crushed with pestle and mortar)
20grams of lightly toasted whole sesame seeds
50grams Caster sugar
100gms Softened unsalted butter
50grams Icing sugar
1 Egg - beaten
Pinch of salt

Sieve together the flour, baking powder and salt, add the crushed sesame.
Separately, cream together the butter and icing sugar and then whisk in the egg. Keep whisking until smooth.
Fold the flour and crushed sesame into the butter and egg mixture.
Stir in the whole sesame seeds and caster sugar.
Add dollops of the mixture to a non-stick surface, about a dessert spoon full each. Space the dollops apart as the mixture will spread when cooking.
Bake at 175°C for 15 minutes (may need a further 5 minutes or so)

As you can see, this recipe is very close to shortbread, it's just that bit lighter and crisper and somehow tastes less sweet.

There is a recipe for matcha shortbread cookies on Chocolate and Zucchini. I have not tried it but I would trust anything that Clotilde makes: http://chocolateandzucchini.com/archives/2009/10/matcha_shortbread_cooki...

Years ago on her TV show, Martha Stewart featured a chef from Takashimaya in New York who made a Matcha Shortbread. I made it at the time and found it a very pretty green, but a little dry. Here's the recipe. Note that it now refers to Chinese powdered green tea rather than Matcha

http://www.marthastewart.com/recipe/green-tea-shortbread-leaves

I live in Japan and regularly make Matcha shortbread.
Using the following recipe and jst add a TBsp or so of Matcha powder
100g flour
50g rice flour
100g butter
50g castor sugar

Squeeze everything together with your hands until it forms a ball.
Knead a little until smooth
Shape , crimp and prick
Bake 180 for about 15-20 mins - watch carefully as can burn quickly - should be still slightly soft when removed