Preheat oven to 400°F. Line a baking sheet with parchment paper.
In a large bowl, combine tomatoes, onion, salt and pepper. Toss well to coat and spread evenly on 1 prepared baking sheet. Roast vegetables in the oven for 25 minutes, stirring twice.
Meanwhile, bring a large saucepan of water to a boil over medium-high heat. Using a slotted spoon, carefully lower eggs into the water one at a time. Cook eggs for 6 minutes, adjusting the heat to maintain a gentle boil. Transfer cooked eggs to a bowl of ice water and chill.
In a medium-sized saucepot, bring water, broth and butter to a boil.
Slowly whisk in polenta. Stirring continuously, cook polenta until it begins to thicken, about 1 minute. Remove from heat and stir in cheese.
Divide polenta into bowls. Top with roasted tomatoes and onions and roasted red peppers.
Gently crack eggs all over and peel. Slice the eggs in half and place 2 halves in each bowl. Sprinkle with additional cheese if desired and serve.