Have all ingredients at room temperature. Combine sugar, water and cream of tartar in a medium, heavy saucepan and cook, stirring, over medium heat until the mixture begins to simmer. Stop stirring, cover, and simmer for 2 minutes to dissolve the sugar, Uncover and wash any sugar crystals from the sides of the pan with a wet pastry brush. Cook, uncovered, until the syrup registers 238 degrees F (soft ball stage) on a candy thermometer. Meanwhile, fill a wide, deep skillet with 1 inch of water and bring to a simmer. In a medium heatproof bowl, preferably stainless-steel, beat on high speed until thick and pale yellow.
Just before the syrup is ready, begin beating the eggs again on medium speed. Beating constantly, pour the hot syrup in a thin steady stream into the eggs at the edge of the bowl. Set the bowl in the skillet of simmering water and stir constantly with whisk until the mixture registers 160 degrees F on an instant-read thermometer. Remove from the heat. Wash the beaters, then beat the hot mixture until it cools to room temperature.
Beat in butter 1 tablespoon at a time until the buttercream is smooth and spreadable. If the mixture looks curdled at any time, continue beating until smooth. If the butter is added too quickly, the mixture may become to soupy; refrigerate it briefly, then resume beating. This keeps, refrigerated, for up to 6 days. Or freeze up to 6 months. To soften chilled or frozen buttercream, break it into chunks with a fork and place in a heatproof bowl in a pan of barely simmering water, or soften in a microwave on low for 15 to 30 second intervals, until some of the buttercream begins to melt. Stir with a rubber spatula until the buttercream is smooth and spreadable. If you oversoften it, you will have to refrigerate it again and resoften it again.
Dissolve 1 tablespoon instant coffee crystals or instant espresso powder in 1 1/2 teaspoons water. Stir most of the mixture into the Buttercream from above.
Melt 2 ounces chopped bittersweet or semisweet chocolate and let cool to lukewarm. Stir into Coffee Buttercream , above, along with 2 tablespoons coffee liqueur, if desired.
Melt 8 to 12 ounces chopped semisweet or bittersweet chocolate with 1 tablespoon water for each 2 ounces chocolate (for example, 4 tablespoons water for 8 ounces chocolate). Let cool to lukewarm. Using a rubber spatula, stir into Buttercream, above, along with 2 or more tablespoons rum, brandy, or liqueur of choice, if desired.
Praline or Nut Buttercream
Stir 1/3 or 1/2 cup nut or praline paste, chopped toasted nuts, or sweetened or unsweetened canned chestnut puree along with 1 to 2 tablespoons liqueur, if desired into Buttercream, above.
Stir 2 tablespoons grated orange zest, 1 teaspoons grated lemon zest, and 1 to 2 tablespoons orange liqueur into Buttercream, above.
Stir 4 teaspoons grated lemon zest into Buttercream, above.