In a double boiler, melt chocolate and butter together over simmering water. Whisk until smooth. Whisk in the half & half. Add ½ cup sugar, whisking as you pour it in. Continue stirring until sugar has dissolved (and isn't grainy), about 30 seconds. Add another ½ cup sugar and stir until dissolved. Then add remaining ½ cup of sugar and stir again.
Cover the pan and cook, stirring occasionally, until the sauce becomes glossy and thickens slightly, about 25 minutes.
3. Cool slightly (15 minutes) and serve warm.
Notes
If you are preparing this recipe as gluten-free, just be sure to use a brand of chocolate that is known to be GF.
If you'd like to make this sauce ahead of time, just pour it into a Tupperware container or a glass jar with a lid and refrigerate until ready to reheat and use.