In a medium nonreactive saucepan set over medium-high heat add the butter and, when melted, add the onions and cook until they are very soft, about 4 minutes. Add the garlic, paprika, Bayou Blast, ground mustard, salt, crushed red pepper, black pepper, and cayenne and cook for 2 minutes. Add the tomato paste and cook, stirring frequently, for 2 minutes, or until the tomato paste begins to brown. Add the water, cider vinegar, and dark brown sugar and stir to combine. Reduce the heat to low and cook until the sauce has thickened and the flavors have come together, 15 to 20 minutes.
Set aside to cool before serving.
The sauce may be made up to one week in advance and refrigerated in an airtight, nonreactive container.
Makes 3 cups