Make the cornbread:
- Preheat oven to 375 degrees and place two (10-inch) cast-iron pans into oven, each filled with 2 ounces vegetable oil or lard. Allow pans to preheat along with oven.
- Combine all dry ingredients together in a large mixing bowl. In a separate bowl, whisk together buttermilk and eggs. Combine wet ingredients with dry, and add melted butter. Adjust consistency of batter with additional buttermilk until the mixture resembles thick pancake batter.
- Pour mixture into preheated cast-iron pans and bake until golden brown and a toothpick inserted in the center comes out clean, 45 to 55 minutes. Remove from pan and set aside to cool.
Make the onions:
- In a heavy-bottomed skillet, melt the butter, allowing it to lightly brown. Add cipollini onions to the pan and cook, turning once until deep brown on each side. Remove from the heat and season with salt. Set aside.
- In another skillet, combine ginger, sugar, vegetable stock, and remaining butter. Bring to a boil, stirring constantly to emulsify liquid and butter. Add white parts of green onions and cook until the liquid in the pan has almost evaporated. Add green parts and cook another 1 to 2 minutes. The onions should be bright green and glazed in the remaining liquid. Remove from heat and set aside.
Pour buttermilk in bottom of bowls and top with cornbread and onions. Serve immediately.