Combine the distilled white vinegar, water, Worcestershire sauce, lemon juice, brown sugar, kosher salt, black pepper, paprika, garlic powder, onion powder, and cayenne pepper in a nonreactive saucepan and whisk to dissolve the sugar.
Bring to a bare simmer over medium heat, stirring occasionally, 3–5 minutes.
Reduce heat to low and simmer gently 10–15 minutes until the sauce darkens, smells mellow rather than sharp, and tastes well-blended.
Remove from the heat and let cool 10 minutes. Use warm as a mop for barbecue or cool completely for bottling.
Store refrigerated up to 1 month; rewarm before serving.