Preheat the oven to 400 degrees . Place the bell peppers skin side down in a 9-inch casserole dish. Add 1 1/2 cups water to the dish, cover with foil and bake for 15 minutes; drain.
Meanwhile, in a large saucepan, melt the butter over medium-high heat. Add the onion, fennel and rice and cook, stirring frequently, until the vegetables are crisp-tender, about 8 minutes. Add the squash, 1 1/2 teaspoons salt, 1/2 teaspoon pepper and 2 cups water; bring to a boil. Lower the heat, cover and simmer until the rice is almost tender, 15 minutes. Stir in the heavy cream.
Spoon 1/4 cup of the rice mixture into each pepper half. Transfer the remaining mixture to the baking dish and nestle the stuffed peppers into the rice. Using a spoon, make an indentation in the center of each stuffed pepper. Crack an egg into each indentation; season with salt and pepper. Bake until the eggs are just set, about 15 minutes.