In the bowl of a stand mixer, beat butter until fluffy. Mix in powdered sugar, salt, whole egg, egg yolk and extract. Sift in cake flour and almond flour and mix until just combined.
Take about a third of the dough and dye it green (I used a combination of green, blue and black to get a nice, evergreen color).
Take a portion of the remaining dough and form it into two logs, each about a half an inch in diameter. Wrap in plastic wrap and freeze for about 20 minutes.
Remove dough from freezer. Using the tip of a butter knife, score the outside of the tubes lengthwise. Take the green dough, divide it in two, and wrap around frozen logs. Re-wrap in plastic wrap and freeze for an additional 20 minutes.
Remove the tubes from the freezer and repeat scoring on the outside of the green portion. Divide the remaining dough into two portions, and wrap around the frozen logs, completely covering the frozen dough. Using your hands, roll until you have a round log. Wrap in plastic wrap and freeze again for about an hour. (If you have a spare paper towel tube, you can stick the dough inside to help keep it round.)
Preheat oven to 350 degrees. Whisk together egg white and water. Remove dough logs from freezer and brush with egg wash. Coat in sprinkles. Slice into half-inch rounds, decorate wreaths with edible sugar balls, and place on parchment or silat-lined baking sheets. Bake at 350 for 7 minutes, lower heat to 330 degrees and bake an additional 7 minutes or until edges begin to barely turn brown.
Cool on wire rack.