Add the first five ingredients for the slaw to a mixing bowl. Stir together the last 7 ingredients in a bowl to make the dressing. Pour the dressing over the carrot-apple concoction and toss everything together until well-combined. Taste the slaw for flavor and add more sea salt or lime juice to taste. Store in a sealed container in the refrigerator for up to 5 days.
Prepare the Black Bean Burgers:
Chop the beet into large chunks and place it in your food processor. Process until beet is reduced to rice-sized peices.
Add the remaining burger ingredients to the food processor and continue processing until very-well combined. You'll need to stop the food processor to scrape the sides several times. The mixture should be sticky - this is normal!
Heat a cast iron (or non-stick) skillet over medium heat with enough olive oil to generously coat the surface. Form the beet mixture into patties while you're waiting for the skillet to heat. Carefully place patties on the hot skillet (I cook 4 at a time), and cook 2 to 3 minutes per side, until hot and crispy.
Serve beet burgers with your favorite toppings on your favorite bun (or go bunless) with carrot slaw. Burgers can be stored in a sealed container in the refrigerator for up to 5 days, or frozen.
Notes
*I recommend using juice sweetened dried cranberries instead of sugar-sweetened for a lower sugar option