Rinse and dice vegetables into 1/2-inch pieces. In a large saucepan, heat the olive oil over medium-high heat. Add the diced vegetables and saute until tender, 8-10 minutes. Season with salt and pepper.

Bring 4 cups water and 1 teaspoon salt to boil in heavy large saucepan. Gradually whisk in polenta; whisk constantly until mixture is smooth and begins to thicken. Reduce heat to medium-low and cook until tender and thickened but still creamy, stirring often, about 30 minutes (note: there can be a real variation in cooking time for polenta, so err on the side of pulling it off the heat too early rather than too late; the kind I used for this recipe thickened up nicely in just 10 minutes, so keep an eye on it). Stir in butter and Parmesan cheese. Season to taste with salt and pepper. Remove from heat.