Grate the garlic and ginger. Finely zest the lime, then juice it.
Heat the olive oil in a medium saucepan over medium heat.
Add the garlic and ginger and sauté until fragrant, about 1-2 minutes.
Pour in the tomato paste, then add the brown sugar, soy sauce, Worcestershire sauce, and apple cider vinegar.
Stir in the curry powder, smoked paprika, red pepper flakes, and salt. Mix well to combine.
Bring to a simmer, then reduce the heat to low and cook for 15-20 minutes, allowing the flavors to meld. Stir occasionally.
Before the end of cooking, stir in the lime juice and lime zest, then cook for an additional 2 minutes.
If you prefer a smoother consistency, use an immersion blender to purée the sauce.
Let cool slightly, then serve with roasted meats, grilled vegetables, or hamburgers.
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