Heat the oven to 350 degrees and coat a 9- by 13-inch baking dish with butter. In a medium bowl, whisk together the first six ingredients.
With a hand mixer or a stand mixer with paddle attachment, beat the butter until smooth. Add the dry ingredients, and blend at medium speed until the mixture resembles coarse crumbs, about 1 minute. Reduce the mixer's speed to low and add the eggs, one at a time, until just blended. Slowly add the buttermilk and blend evenly.
Pour the batter into the pan, and bake until the top is golden brown and a toothpick inserted in the middle comes out clean, about 20 minutes. Let bread cool then divide in half.
Crumble the cornbread half in an even layer onto a baking sheet (reserve the remaining cornbread for another use). Heat the oven to 350 degrees, and coat another baking sheet with cooking spray.
In a small pan over medium heat, warm the oil. Add the onions and sauté until soft, about 5 minutes. Add the garlic and cumin, season with salt and pepper, and sauté for 1 minute more. Set aside.
In food processor, pulse the beans, rice, and cilantro until well blended. Add the egg, pulse, then add the cooked onion mixture, along with 2 cups of the crumbled cornbread; pulse until evenly combined.
Form the mixture into 1-inch balls. Roll each in the remaining cornbread crumbs to coat, and place them on the prepared baking sheet. Bake until golden brown, about 20 minutes.
Meanwhile, in a small bowl, stir together the dipping sauce ingredients. Serve the black-bean bites warm, with the sauce on the side.