Creamy Goat Cheese Grits with Roasted Brussels Sprouts and Squash and Poached Eggs

Brussels sprouts, ends trimmed and quartered

butternut squash, peeled, and diced into 1/2-inch cubes

sprigs of fresh thyme, plus more for garnishing

fresh sage leaves

extra virgin olive oil

kosher sea salt

freshly ground black pepper

and 1/4 cups whole milk

kosher sea salt

unsalted butter, divided

stone ground corn grits (I used rainbow stone ground grits from a local Chicago brand called Baker Miller)

to 3 ounces soft goat cheese, room temperature

freshly ground black pepper