Preheat the oven to 350 degrees F. Butter 8 (4 by 2 1/2-inch) ramekins.
Melt the butter in a medium saucepan over low heat. Add the flour, stirring constantly until completely incorporated. Slowly stir in the half-and-half. Cook for about 2 minutes whilst stirring with a wire whisk until thickened and smooth. Add the chevre and stir until melted. Remove from the heat and beat in the egg yolks, 1 at a time. Transfer to a large bowl and sprinkle with salt and black pepper (the mixture should be slightly over seasoned).
In a medium bowl, beat the egg whites and cream of tartar with an electric mixer to soft peaks. Do not overbeat. Carefully fold the egg whites into the cheese mixture. Divide the mixture among the prepared ramekins, filling them to about 1/4 inch from the top. Carefully place the filled ramekins in a shallow roasting pan. Pour enough hot water into the pan to come 3/4 inch up the sides of the ramekins. Bake until the tops are set and brown, 40 to 45 minutes.
Remove from the water bath and allow to cool to room temperature. At this point, the puddings can be kept at room temperature for up 2 hours, or covered in plastic wrap and refrigerated for up to 2 days.
To serve, preheat the oven to 400 degrees F. Run a knife around the edges of the puddings. Gently unmold each one into the palm of your hand and place right side up on an ovenproof dish. Drizzle 1 tablespoon heavy cream over the top of each souffle. Bake until the cream is slightly brown and bubbly, 15 to 20 minutes.
Ladle some of the Carrot and Cumin Sauce onto a dish and place a souffle on top. Garnish with any small crumbs of chevre and fresh chives and serve.
For Carrot Sauce:
Peel and coarsely chop the carrots, onion and garlic and place into a sauce pan along with the butter, salt and pepper and cumin. Fill with water to cover. Simmer until the vegetables are soft. Drain the excess water, reserving 1 tablespoon, and puree the vegetables in blender until smooth, adding reserved liquid if needed. If necessary, add more salt and pepper and cumin, to taste.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.