Preheat oven to 420 degrees. Arrange washed and chopped vegetables on a sheet tray. Drizzle with olive oil and 1 teaspoon of salt. Bake for about 30 minutes, or until veggies are tender.

In a large Rondeau pan or wide bottom pot, bring 8 cups of water to a boil, reserving the last cup for later. Mix in 2 teaspoons of salt and pour in the polenta. Lower the heat to medium-low and stir to incorporate. Frequently over the next 20 minutes, stir the polenta. Be careful, very hot steam gets trapped and can bubble out while you mix.

Add the remaining cup of water, mix until it begins to bubble again, and add the parmesan and white pepper. Mix to combine. Add the butter and mix until it is fully melted. Cover the polenta, going back to stir a few times, for 10 minutes while you prepare the poached eggs.

In a small saucepot, fill about halfway with water and bring it a boil. Crack your eggs one at a time into a small bowl that is easy to pour from (but without a spout). Turn the heat to low, and add the vinegar.

Once the water is no longer boiling but is at a nice simmer, use a wooden spoon to swirl the water in one direction. Gently pour the cracked egg into the water. Gently swirl the water a few more times while it cooks for 3 minutes.

Note: If you are skilled at poaching eggs, feel free to cook them together, without swirling the water. If you are not skilled, I recommend repeating step 4 with each egg, refreshing the water and vinegar each time.

Once each component is ready, assemble each plate with a heaping portion of polenta, veggies, and 1 or 2 poached eggs. Top generously with dill, and garnish with freshly cracked salt and pepper.