While none of the recipes we received included eggs, this one from Pam Coloton, Buchanan, Virginia, seems to come closest to what Betty remembers.
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Old-Fashioned Rice Pudding Recipe
1/3 cup uncooked rice
4 cups milk, scalded
1/4 teaspoon salt
1/4 cup sugar
2 tablespoons butter
Heat oven to 300°F.
In 6 1/2-by-10 1/2-by-1 3/4-inch flat baking dish, combine all ingredients. Place dish in oven and bake for 1 1/2 hours, or until rice is perfectly tender and pudding is thick and creamy, not dry. Stir every 15 minutes with fork, carefully turning under brown top and scraping down edges.
Serve hot or cold. Yields 5 servings.