Pour the red beans, navy beans, brown sugar, and ½ of the drained Rotel tomatoes into a large mixing bowl. Set aside.
Pour the remaining Rotel tomatoes, garlic, onion, celery, bell pepper, Tabasco pepper, hot sauce, parsley, celery leaf, lime juice, lime zest, and salt and pepper into a blender or food processor.
Pulse until liquefied.
Pour the mixture into the mixing bowl holding the other ingredients. Add the tapioca flour.
Mix by hand until well-incorporated. (The mixture will thicken as you stir it.)
Bake for 20 minutes, then remove from oven, and let sit for 20 minutes before serving. (This is very important as the sit time lets the flavors intermingle. Otherwise, you will taste the brown sugar in the dip and not the rest of the seasonings.)