Peel the red onions and slice them into thin rings. Mince the garlic finely.
In a large saucepan, heat the olive oil over medium heat. Add the onions and caramelize over low heat for 15-20 minutes, stirring occasionally, until golden brown and sweet.
Add the minced garlic to the caramelized onions and sauté for another 2 minutes, until fragrant.
Pour in the beer, then stir in the tomato paste, brown sugar, Worcestershire sauce, balsamic vinegar, and Dijon mustard. Mix thoroughly.
Season with smoked paprika, salt, and pepper. Let the sauce simmer over low heat for 20-25 minutes, or until thickened.
Once thickened, remove from heat and let cool slightly. Then, blend until smooth with an immersion blender or in a regular blender if you prefer a smoother consistency.
Pour into a clean jar or serve immediately with grilled meats and vegetables. Can be stored in the refrigerator for up to a week.
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