In a stand mixer, beat together butter, sugar, salt and vanilla for 2 minutes on medium speed, scraping bowl occasionally.
Press cooked egg yolks through a fine sieve with the back of a spoon into the mixing bowl and beat for 2 minutes more, ensuring that the yolks are fully incorporated.
Stir flours to blend, then add to batter with citrus zests and thyme. Mix lightly only to incorporate, do not over mix.
Form into a disc ½-inch thick - this will facilitate easier cutting into shapes when cold.
Cover with plastic and refrigerate overnight. This allows the flour to rehydrate and chills the butter, reducing spreading when baking.
Remove from the fridge and place on a floured surface, sprinkle top lightly with flour, roll top smooth with rolling pin and cut out with floured cookie cutter as desired.
Heat oven to 350 F.
Place cookies on parchment-lined baking sheets.
Refrigerate cut cookies 10-15 minutes if they start to warm to room temperature.
Dock holes in each cookie with a skewer or fork to release steam, sprinkle with sugar or other embellishments if desired, and bake until lightly browned, approximately 16-22 minutes.
Let cool completely on a wire rack before drizzling. After cooling, drizzle with glaze and sprinkle with leftover zest.