Place the grated beets, dates, almonds, and ginger into a food processor. Pulse several times until the mixture is finely chopped but not a complete paste—you want some texture.
Transfer the beet mixture to a large bowl.
Add the bulgur and a generous sprinkle of salt and pepper.
Pour in the boiling red wine or water, stir in the mustard and cayenne (if using), and mix to combine.
Cover the bowl with a plate and let it steep for 20 minutes, allowing the bulgur to soften.
Uncover the bowl, taste the mixture, and adjust the seasoning if necessary. If the mixture seems too wet to form patties, stir in a tablespoon or two of flour to help bind it.
Shape the mixture into 4 to 6 evenly-sized patties. For best results, you can chill the patties for 30 minutes to help them firm up.
Heat the olive oil or butter in a large skillet with a lid over medium heat.
Once the pan is hot, carefully place the burgers in the skillet.
Cook undisturbed for about 5 minutes, until a deep brown crust forms on the bottom. Carefully flip the burgers, cover the pan, and cook for another 5 minutes on the other side.
Serve immediately on buns with your favorite toppings, or let cool completely to refrigerate or freeze for a future meal.
Don't over-process the burger mixture in step 1. A little bit of texture from the nuts and beets makes for a much more satisfying bite.
Chilling the formed patties in the refrigerator for at least 30 minutes before cooking helps them hold their shape beautifully in the pan.