Put on gloves before handling the scotch bonnet peppers. Roughly chop the scallions, onion, garlic, ginger, and scotch bonnet peppers.
Add the allspice berries and cinnamon stick to a dry skillet over medium heat. Toast for 60–90 seconds, shaking constantly, until fragrant. Let cool slightly, then grind to a coarse powder.
Add the chopped aromatics, toasted spices, nutmeg, brown sugar, soy sauce, lime juice, oil, salt, and black pepper to a food processor or blender.
Blend on high, scraping down the sides every 20–30 seconds, until a mostly smooth, thick paste forms. Add a tablespoon of water if it's too thick to blend.
Taste a small amount. Add more brown sugar or onion if it's too hot; add another pepper if you want more heat.
Transfer to a clean glass jar. Let sit at room temperature for 15–20 minutes before using, or refrigerate immediately.