Step 1In the bowl of a food processor, combine the pepper, nutmeg, allspice, cinnamon, cloves, salt, sugar, peppers, garlic, ginger, scallions, lime zest and juice, vinegar, rum and oil. Pulse a few times to form a coarse paste.
Step 2Transfer the mixture to a medium, heavy-bottomed saucepan and simmer for 3 to 5 minutes, stirring frequently, to marry the flavors.
Step 3Remove from heat. Place the mixture back in a food processor or blender and blend to form a smooth sauce, thinning as desired with one-half to 1 cup water. Strain if desired. To store, refrigerate the sauce in a covered glass bottle or jar.