Place cabbage in a single layer across a platter or baking sheet. Brush both sides of the cabbage with the oil and season with salt and pepper.
Heat a grill over medium high heat (about 400 - 450 degrees F). When hot, gently place the the cabbage on the grill and cook, covered, until tender-- about 8 minutes total, turning halfway through.
Meanwhile, you will also want to grill the bratwursts until golden brown on both sides, 2-3 minutes a side.
One a large platter, plate the grilled cabbage and drizzle with 2 tablespoons of lemon juice. Plate the sausage alongside the cabbage and a bowl of the sauteed onions. Sprinkle the chives all over (optional). Serve with lemon wedges, and a side of your favorite grainy mustard and dijon mustard. You can also serve with sauerkraut, too, if desired!