Heat vegetable oil in large saucepan over medium heat. Cook and stir onions in the hot oil, until nearly dark brown, 10 to 15 minutes.

Pour wine into the saucepan, bring to a simmer and cook until reduced by half, about 1 minute; remove pan from heat.

Stir currant jelly, orange juice, orange zest, lemon zest, lemon juice, brown sugar, black pepper, mustard powder, ginger, cayenne pepper, and salt into onion mixture until combined.

Bring sauce to a boil; remove from heat.