Combine all ingredients in a small saucepan over medium-high heat and cook, stirring occasionally, until sugar has dissolved completely. Remove from heat and allow to steep at least 4 hours, up to overnight. Strain out solids. Syrup will keep, refrigerated in an airtight container, for 4 weeks.
FOR THE EGGNOG:
In a blender, or using an immersion blender, blend together eggs, almond milk, and simple syrup until thoroughly emulsified.
Stir in cognac, sherry, and nutmeg. Refrigerate eggnog, stirring occasionally, at least 4 hours and preferably overnight. If eggnog breaks, re-blend just before serving.
Serve cold in punch cups, garnished with freshly grated nutmeg.