Warm your baked beans in a saucepan over low heat. Stir occasionally to prevent sticking. Keep them covered so they stay hot while preparing the polenta.
Cut the kernels off the fresh corn cobs. Melt butter in a large pot over medium heat. Add corn and sauté until slightly tender and fragrant.
Pour broth (or water) into the pot and add salt. Bring to a gentle boil, then slowly whisk in the polenta. Reduce heat to low to maintain a steady simmer.
Stir frequently to avoid lumps and ensure even cooking. The mixture will thicken gradually and become smooth and creamy.
Turn off the heat once the polenta reaches a soft, thick consistency. Stir in freshly grated cheese until completely melted and creamy.
Spoon the warm polenta into bowls. Top generously with heated baked beans. Finish with cracked black pepper and serve immediately.