Mix 2 cups water, the orange juice, honey, sugar, lemon zest and juice, and cinnamon in a medium saucepan. Add the apricots and bring to a simmer over medium heat, stirring occasionally. Partially cover the saucepan with the lid and simmer until the apricots are tender, about 10 minutes.
Remove from the heat and add the thyme and nutmeg. Cool until warm (or cool, cover and refrigerate until chilled). Serve, spooned over ice cream and topped with long thin strips of lemon zest, if desired.