1. Preheat grill to 300-350F (medium) heat. Cook first 3 ingredients in a 2-qt heavy saucepan over medium heat, stirring constantly, 2 min.
2. Cut each onion crosswise into 3 slices. Grill onion slices, covered with grill lid, 32 minutes, turning every 4 minuts and basting with bourbon mixture with each turn during last half of grill time. Remove from grill, wrap in aluminum foil and let stand for 10 min.
3. Meanwhile, whisk together vinegar and next 5 ingredients. Add oil in a slow, steady stream, whisking constantly until smooth. Whisk before serving.
4. Sprinkle tomato slices with salt and pepper. Place 1 tomato (or stack 2) on each of 4 plates. Tope each with 1 onion slice and spread with 1 1/2 tsp goat cheese. Tope ach stack with 2 basil leaves and 1 bacon piece. Repeat layers once, Top with remaining onions. Spoon 1 Tbsp vinaigrette over each stack.
5. Toss greens with 3 Tbsp vinaigrette and serve immediately with sweet onion stacks.
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