Char the pepper over an open flame on the stovetop or under the broiler (if using the broiler, crack open the oven door to allow steam to escape, and switch the temperature to 425 degrees after charring). Place in a bowl, cover and let cool. Peel and seed the pepper, then quarter lengthwise and slice into very thin strips.
Preheat the oven to 425 degrees . While the pepper is charring, in a large skillet, heat the EVOO, 1 turn of the pan, over medium-high heat. Add the sausage and cook, breaking up the meat with a spoon, until browned, 10 to 12 minutes.
Meanwhile, in a large saucepan, bring the stock and milk to a low boil. Whisk in the polenta and season with salt, pepper and the fennel. Cook, whisking, until thickened, 2 to 3 minutes. Stir in 1 cup cheese and the butter.
Spread the sausage in a casserole (or individual baking dishes). Fill with the polenta and hollow out 6 holes; crack an egg into each one. Top with the remaining 1/2 cup cheese and bake until set, 15 to 20 minutes. The eggs will be soft to medium (touch the yolks for doneness-a slight springback means serve me!). Garnish with the roasted red pepper strips.