Preheat the grill to medium.
In a large baking pan, place the onions. Lightly coat both sides with oil and season with salt and pepper.
When the grill is hot, add the sausages and cook, turning occasionally, until cooked through, 10 to 12 minutes. Remove from the heat and place in the middle of a large platter.
While the sausages are cooking, add the onions to the grill. Cook, turning twice, until tender and slightly charred, about 5 minutes per side, keeping the rings together. Remove from the grill and place on the edge of the platter around the sausages. Sprinkle onions lightly with balsamic vinegar and fresh thyme. Scatter a little anise hyssop over platter, if using. Serve immediately.
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