Preheat oven to 375º F (adjusting for your own oven, especially if you use convection), and prepare two cookie sheets with silicone liners or parchment paper.
In a medium bowl, stir or whisk the flour, xanthan gum, baking soda, cream of tartar, salt, and anise.
Mix the shortening, 3/4 c sugar, and brown sugar with the paddle blade in your stand mixer until it's a light, creamy, cloudy dream -- it'll take a couple minutes.
While that's mixing, whisk the egg replacer and 2T of rice milk together and let it sit for about a minute to thicken
Then add the egg replacer mixture and the vanilla to the shortening mix and stir until just combined.
With the mixer on low, alternate adding half the flour mixture, then half the rice milk. It should go without saying, but scrape the bowl down a couple times (and especially before the last bit if rice milk goes in) to make sure it all gets combined. When you toss that last bit of rice milk in, it'll come together pretty quickly into a nice thick lump.
Combine the 2 T sugar with the cinammon and anise seed in a small bowl.
Use your hands to roll the dough into golf-ball-sized balls, then roll in the sugar mixture and arrange on the cookie sheet a few inches apart (they will spread during baking, so give 'em plenty of room. I do 3x4 on a half-sheet pan).
Bake (each pan separately) for 10 minutes. They should spread and crack to give you a peek at the yummy fluffy centers. Let them cool in the pan for 10 more minutes, then remove to a cooling rack.