Stir brown sugar, lemon-lime soda, orange liqueur, cloves, allspice, salt, and black pepper together in a saucepan; bring to a simmer and cook until glaze is reduced by 1/4, about 10 minutes.

Strain through a fine-mesh sieve into another saucepan. Bring mixture to a simmer again and cook until glaze is about the consistency of maple syrup, about 10 minutes more.