Combine everything into a large pot and bring to a boil, let it go for 45 minutes (or until beets are soft). Scoop out beets and set aside. Remove half of the liquid from the pot (be careful not to remove any of the spices).
Bring liquid back to a boil and reduce it down to 1 cup. While the liquid is reducing, heat your grill to maximum heat (you can coat the rack with a little oil to keep the beets from sticking).
Grill the beet slices, about 1 minute per side. Now that the liquid is reduced, add 1 cup packed brown sugar and stir to dissolve.
In a blender, combine beets, and the cooking liquid syrup (still including the vanilla bean, cinnamon and all other spices) and blend until smooth (you may have to do this in batches if everything won't fit in the blender).
Keep refrigerated or you can freeze.
Shake with ice, serve in glass rimmed with sal de gusano and garnish with a lime.
Put all ingredients in a blender and puree until smooth.