Preheat the oven to 350 degrees.
Add the sliced carrots to a saucepan with water and boil until soft. About 15-20 minutes. Drain and then let the carrots cool.
Butter a 9x9 baking dish and set it aside.
Melt the butter in a large saute pan over medium heat. Add the red pepper and onion and cook until the onions are translucent.
Add the salt, pepper, sugar, and flour and mix until combined. Let cook for two minutes, stirring occasionally.
Heat the milk in the microwave for 35 seconds, then add it to the onion and pepper mixture half at a time, stirring to incorporate each time. Cook this mixture for 1 minute and then remove it from the heat.
Add 1/2 of this mixture to the carrots (it will help them mash), and then, using a potato masher, mash the carrots until they are chunky —do not mash them to a puree; you want them chunky.
Whisk the egg in a separate bowl and add it to the mixture along with the parsley. Then, add the rest of the onion and pepper mixture until it is combined.
Transfer the carrot mixture to the baking pan and bake uncovered for 1 hour.
While the carrot mixture is baking, mix the melted butter and sprinkle the panko breadcrumbs on top when there are 20 minutes left to the baking time.
Remove from the oven and serve.