Preheat the oven to 325 degrees F.
In a baking dish, combine the parsnips, 2 tablespoons of the butter, the brown sugar, cinnamon, and allspice and cover tightly with aluminum foil. Bake until the parsnips are tender, about 45 minutes. Remove from the oven and uncover.
In a large skillet, melt 1 tablespoon of the butter over medium heat. Add the pears and cook, stirring, for 3 minutes. Add the liqueur and tilt the pan to ignite the contents. (Alternately, remove from the heat, light with a match, and return to the heat.) Cook while flaming for 2 minutes. Transfer to a food processor.
In a skillet, melt the remaining 3 tablespoons of butter over medium heat. Cook, swirling the pan, until the butter is golden brown and has a nutty aroma. Add the browned butter, baked parsnips and their cooking liquid to the food processor. Puree on high speed for 30 seconds. Add the sour cream, salt, and pepper and process until smooth. Serve immediately or cover to keep warm until ready to serve.
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