Directions

1. for the pesto: Mix olives and fresh herbs in a medium-sized bowl. Stir in olive oil and season with salt and pepper. Mix until homogenous. Set aside.
2. for the polenta: Heat water in a large pot, when boiling, slowly pour in polenta. Lower the temperature to simmer and cook for about 20-25 minutes, until polenta has absorbed the water. Take pot off flame and stir in shredded cheese and salt. Season with salt and pepper. Cover and set aside until plating.
3. for the poached eggs: Crack eggs into a small bowl, set aside. Heat another medium-sized pot with water, adding a sprinkle of salt and teaspoon of vinegar to water. When water is at a boil, slip the four eggs into the water bath, swirling with a spoon to help eggs form into solid shapes. Cook for about four minutes for a slightly runny center. Here's a great tutorial on The Kitchn, in case you need more help poaching the eggs.
4. to assemble the dish: ladle about 1 1/2 cups of the polenta into a large bowl, add an egg to each bowl, garnish with the olive-herb pesto. Serve with extra olive oil and lots of salt and pepper.