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1
Combine carrots, rutabaga, onion, chicken stock, 3 tablespoons butter, brown sugar, and nutmeg in a large saucepan; bring to a boil. Reduce heat, partially cover saucepan with a lid, and simmer, stirring occasionally, until vegetables are very tender, about 45 minutes.
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2
Transfer vegetables using a slotted spoon to a food processor or blender. Continue to cook remaining broth mixture in saucepan over high heat, stirring constantly, until liquid reduced to about 1 tablespoon, 2 to 3 minutes. Add reduced broth mixture to vegetables in food processor; blend until very smooth. Transfer mixture to a bowl and cool to room temperature.
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3
Stir eggs, flour, baking powder, salt, and pepper into pureed vegetable mixture until evenly combined; spoon into a buttered 6-cup casserole or souffle dish.
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4
Melt remaining 1 tablespoon butter in a saucepan over low heat; stir in pecans until fragrant and coated, 1 to 2 minutes. Spread buttered pecans around the edge the vegetable mixture, creating a border. Cover dish with plastic wrap and refrigerate, 8 hours to overnight.
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5
Bring vegetable mixture to room temperature, about 30 minutes before baking.
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6
Preheat oven to 350 degrees F (175 degrees C). Remove plastic wrap from casserole dish.
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7
Bake in the preheated oven until puffed, set in the middle, and golden brown, about 30 minutes.