To a large saucepan, add the broth and milk. Bring to a simmer, and stir in the polenta. Reduce the heat and cook until the liquid is absorbed and the polenta is cooked, about 10 minutes. Remove from heat. Add the butter and cheese. Stir until melted. Set aside.

To a large saute pan, add the sausage. Cook until just browned on the outside, and add the mushrooms and shallot. Cook until the veggies are tender and the sausage is no longer pink. Add the polenta mixture to the pan with the sausage and mushroom mixture. Stir to combine. Pour the mixture into a large baking dish and cover. Place in the refrigerator for about and 2 hours to chill.

Meanwhile, preheat your oven to 375 degrees F. Place the polenta, covered, in the oven and bake for 40 minutes. Remove from heat. Reduce heat on the oven to 325 degrees F.

Crack the eggs on top of the polenta. Sometimes, it's easier to crack the eggs into a bowl first to make sure they are not broken and you get out any unwanted shell pieces. Bake, uncovered, until the eggs are set, about 12 minutes. Remove from heat and sprinkle with black pepper and chopped cilantro. Enjoy!