Gently melt the 61-percent chocolate in a heatproof bowl in the microwave. Transfer to a food processor. Bring the cream and corn syrup to a boil and slowly stream into the melted chocolate with the machine running. Slowly stream in the absinthe. Add the butter to the running processor. Transfer to a bowl or shallow dish and let set up overnight in a cool place, use the fridge only if you have to.
Line baking sheets with parchment paper. Using a very small scoop, scoop enough ganache to make a 1 1/2-inch ball and quickly roll in your hands, dropping the formed balls onto the prepared baking sheets. If the balls are soft, let them sit for 30 minutes in the fridge to become firm and easier to handle.
Temper your chocolate: Place two-thirds of the dark chocolate in a microwave-safe bowl. Microwave on medium in 30 second intervals until fully melted, about 3 minutes. The temperature of the chocolate should be around 120 degrees F. Add remaining one-third of the chocolate and stir until fully incorporated. Keep stirring until the chocolate reaches 85 degrees F. You can test it by holding the chocolate covered spatula to your lower lip. When it no longer feels warm, the chocolate is ready. You can warm it SLIGHTLY, to 90 degrees F, to make it more fluid. This can be done by microwaving it in 2 second intervals. I am not joking - 2 seconds, no more! Keep the chocolate on a heating pad set to low if you are not going to use it for a while. Make sure the temperature stays between 85 and 90 degrees F. If it goes over, you will have to start the process again. And you DON'T want to do that.
Using gloves, spread a little bit of the tempered chocolate in the palms of your hand. Roll the truffles one at a time to coat. This will make a very thin shell. Place on the prepared baking sheets and sprinkle with coarse sugar to decorate. Store in a cool dry place.