Polenta with Shrimp Gravy and Poached Egg

• 1 tablespoon olive oil
• 1/2 red bell pepper, diced
• 1/2 white onion, diced
• 2 cloves garlic
• 1 pound medium shell-on shrimp, deveined and peeled; shells reserved
• 2 tablespoons brandy
• 10 cups water, divided
• 1/2 cup polenta
• Salt and pepper to taste
• 1 1/2 tablespoons butter
• 1 1/2 tablespoons flour
• 4 eggs
• 2 tablespoons white vinegar
• Sliced scallions for garnish

Heat the oil in a large pot over medium heat. Add the peppers, onions, and garlic. Sauté until tender, about 5 minutes. Add the shrimp shells and cook until they are completely pink, about 2 minutes. Add the brandy and simmer until the liquid has evaporated, about 1 minute. Add 6 cups of the water. Let return to a simmer. Cover and continue simmering for 45 minutes. Strain the stock and discard the shrimp shells. Reserve.

Bring the remaining water to a boil in a medium pot. Slowly whisk in the polenta. Simmer over low heat for 45 minutes, whisking often. Season with salt and pepper.

Melt the butter in a large pot. Add the flour and stir to fully incorporate. Cook over medium-high heat, stirring, until the mixture is golden in color, about 7 minutes. Add the reserved shrimp stock and bring to a boil. Boil until the gravy has thickened slightly, about 5 minutes. Reduce to a simmer. Add the shrimp and simmer until the shrimp are cooked through, about 3 minutes. Remove from the heat and reserve.

Bring a large pot of water to a boil. Add the vinegar and season with salt. Add one of the eggs and poach for 3 to 4 minutes. Remove with a slotted spoon and transfer to a plate. Repeat with the remaining eggs.

To serve, divide the polenta among 4 serving dishes. Top each serving with a poached egg. Spoon some gravy and shrimp over the eggs. Garnish with scallions.