Heat the oil in a pot over medium heat. Add the onions and cook, stirring, until very tender and almost sticky, about 10 minutes. Stir in the remaining ingredients, except the sausages. Gentle simmer until the vinegar thickens and becomes syrupy, about 5 minutes. Cool to room temperature; transfer to a serving dish, cover and store in the fridge until the sausages are ready.
Preheat the oven to 375 degrees F. Place the sausages in a parchment paper-lined roasting pan. Roast, turning once, until golden and cooked through, about 20 to 25 minutes. Serve the sausages with a generous spoonful of the relish alongside. Any leftover relish will keep in the fridge for up to a week.