From Farmer John’s Cookbook

Butter for greasing the baking dish
2 1/2 cups vegetable or chicken stock
1/2 pound carrots (about 3 medium carrots)
1/2 cup heavy cream
1/2 cup milk
1 tbsp unsalted butter
2 tbsp flour
1/4 tsp freshly ground nutmeg
1/8-1/4 tsp cayenne pepper
3/4 cup uncooked short-grain white rice
Salt
Freshly ground black pepper

Preheat the oven to 375.  Lightly coat a 6-cup baking dish with butter.  Bring the stock to a boil in a medium pot.  Add the carrots and reduce the heat to a simmer; cook, uncovered, until very tender, 10-12 minutes.  Drain carrots, reserving the stock.  Let the carrots cool for 5 minutes.  Transfer the cooked carrots to a blender or a food processor.  Add the cream; process to a smooth puree.  Heat the milk in a small pot over medium-low heat, stirring occasionally, just until bubbles form at the edge, but do not boil.  Melt the butter in a medium pot over low heat.  Stir in flour; cook, stirring constantly, for 2 minutes.  Gradually whisk in the hot milk and then the stock.  Add the carrot puree, nutmeg, and cayenne to taste.  Turn the heat up to high and bring the mixture to a boil; add the rice, and season with salt and pepper to taste.  Cover, reduce the heat to low, and cook for 12 minutes.  Remove the pot from heat. Transfer the ingredients to the prepared baking dish and bake for 15 minutes.