Line an 8-inch square baking pan with aluminum foil that extends over the sides. Coat the foil with 1 tablespoon of the butter. Set aside.

In a 3-quart heavy-bottomed saucepan over low heat, cook the cream, half-and-half, sugar, salt, and the remaining 8 tablespoons butter until the sugar is dissolved and the butter is melted (about 5 minutes), stirring constantly with a long-handled wooden spoon or heat-proof spatula. Bring the mixture to a boil over medium heat, then brush down the sides of the pan with a pastry brush dipped in warm water to prevent the sugar from crystallizing. Place a sugar thermometer in the pan and cook the mixture without stirring until it registers 238 degrees F. on the thermometer (about 15 minutes).

Remove the pan from the heat, remove the thermometer, and place the thermometer in warm water to cool. Sprinkle the back of a baking sheet with cold water and immediately pour the hot mixture onto it. Do not scrape out the bottom of the pan. Let the mixture cool until it registers 110 degrees F. on the thermometer (about 15 minutes). (If you have a marble slab, follow the above directions; the fudge will cool in about 5 minutes.)

Transfer the mixture to a 2 quart mixing bowl, add the vanilla, and beat with a long handled wooden spoon until it thickens and loses its shine (10 to 15 minutes). Add the coconut after beating and mix until it is well blended in. (You can also use a mixer.)

Turn the fudge into the prepared pan. Use your fingertips to even the top and to press the fudge into the corners of the pan. Place the pan of fudge on a cooling rack and let it set completely at room temperature (1 to 2 hours).

Remove the fudge from the pan by lifting out the foil. Invert the fudge onto a cutting board, peel off the foil, and invert the fudge again. With a large chef’s knife, cut the fudge evenly into 1-inch squares. Store in a tightly covered container between layers of waxed paper in the refrigerator for 1 month or at room temperature for 10 days. Best served at room temperature.