Preheat oven to 375˚F.
Place all the vegetables onto a sheet pan, drizzle with oil, sprinkle with thyme, and season with salt and pepper. Toss together and spread in a single layer.
Roast vegetables for 30 to 40 minutes or until fork tender.
While the vegetables roast, pour milk into a saucepan and place over medium-high heat.
Bring milk to a boil and begin whisking in the polenta.
Lower the heat to medium and simmer for about 20 minutes or until the mixture thickens. Remove the polenta from the heat and stir in the butter and grated parmesan. Season with salt and pepper.
Pour polenta into a large serving bowl or divide into individual bowls, top with mixed roasted vegetables and finish with crumbled goat cheese. Serve.