For the cheesy polenta:

1 tablespoon olive oil

¾ cup finely chopped onion

3 cloves garlic, finely chopped

2 cups chicken or vegetable broth

2 cups milk

1 cup polenta (coarse cornmeal)

½ cup grated parmesan cheese (or other melting cheese)

¼ teaspoon salt

¼ teaspoon ground black or white pepper

3 tablespoons unsalted butter

For the poached eggs:

6 large eggs

Optional garnishes/add-ins:

1 cup canned pumpkin puree

2 teaspoons chopped fresh parsley or chives

½ teaspoon dried sage or rosemary

4 tablespoons toasted pumpkin seeds

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Heat olive oil in a heavy pot over medium heat. Add onion and cook until translucent, about 3 minutes. Stir in garlic and cook 1 minute more.
Add broth and bring to a boil. Slowly whisk in polenta to prevent clumping. Reduce heat to low, cover, and cook for about 20 minutes, stirring occasionally. Add extra liquid if too dry.
When creamy, stir in butter, parmesan, and optional pumpkin puree. Season with salt and pepper.
To poach eggs: Bring a saucepan of water to a gentle simmer. Add eggs using a poaching insert or crack directly into simmering water with a splash of vinegar. Cook for ~3½ minutes for runny yolks.
Spoon ~¾ cup of polenta into bowls, top with a poached egg, and garnish with parsley, chives, or pumpkin seeds if desired. Serve warm.