Preheat oven to 400°F. Place the bell peppers skin side down in a 9-inch casserole dish. Add 1 ½ cups water to the dish, cover with foil and bake for 15 minutes. Drain.
Meanwhile, in a large saucepan, melt butter over medium-high heat. Add onion, celery and rice, stirring frequently until the vegetables are crisp-tender, about 8 minutes. Add squash, salt, 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 cream and cheese until combined.
Spoon ¼ cup of the rice mixture into each pepper half. Transfer the remaining mixture to the baking dish and nestle the stuffed peppers into the remaining rice. Using a spoon, make an indentation in the center of each stuffed pepper. Crack an egg into each indentation. Season with celery salt. Bake until the eggs are just set, about 15 minutes.