Prep the aromatics: Trim and roughly chop the scallions. Peel and roughly chop the half onion and ginger. Wearing gloves, stem the Scotch bonnets and remove some or all seeds to control heat, then roughly chop. Roughly chop the garlic.
Start the paste: Add the scallions, onion, Scotch bonnets, garlic, and ginger to a blender or food processor. Pulse to a coarse paste.
Season and blend: Add the thyme leaves, allspice, cinnamon, nutmeg, brown sugar, kosher salt, black pepper, apple cider vinegar, lime juice, soy sauce, and oil. Blend until smooth and thick, 30–60 seconds, scraping down the sides as needed.
Adjust: Taste and adjust seasoning for salt and brightness. For more heat, blend in some reserved chile seeds.
Rest: Let the sauce sit 30 minutes at room temperature to meld. For later use, transfer to a clean jar and refrigerate up to 1 week.
Use: For marinating, use about 1/2 cup per pound of chicken or pork and marinate 4–12 hours refrigerated. If serving as a table sauce, reserve a clean portion before marinating or bring any sauce that touched raw meat to a full boil for 1 minute before serving.