In a large bowl, cover the beans with warm water by 3-inches and soak for at least 6 hours, ideally overnight. Drain and set aside.

Cut off about 1-inch from the top of each garlic head to expose the cloves and remove any loose peel. Heat the olive oil in a Dutch oven over medium heat. Add the garlic heads cut side down and cook without disturbing until browned, about 3 minutes. Add the red pepper, if using, and let it fry for about 1 minute. Add the soaked beans, broth, sage, rosemary, and bay leaf and bring to a simmer. Partially cover and cook until the beans are tender, 45 to 55 minutes.

Adjusting the heat as needed to keep the beans at a low simmer. Add additional broth if needed to keep the beans just barely covered.

Remove the garlic heads, sage, rosemary, and bay leaf. Add salt to taste. Stir in the chard stems and continue cooking; partially covered, for 10 minutes, stirring occasionally. Squeeze the garlic heads to remove the cloves and gently mash the cloves. Stir in the mashed garlic and chard leaves and cook for another 5 minutes. Taste again and add additional salt, if needed. Cover the pot and remove from the heat.

Melt the butter in a large skillet over medium heat, swirling to coat the pan. Add the cornbread slices and cook until browned and toasted, about 3 minutes per side.

Place a slice of the toasted cornbread in the bottom of a shallow bowl. Ladle the brothy white beans and chard over the toast and serve with a generous grating of Parmesan and lashings of olive oil.