2. With the skin on, cut the shallot in half lengthwise. Spray a baking sheet with non-stick spray. Drizzle the shallot with a bit of the olive oil and place them on the baking sheet cut side down.
3. Roast in the oven until the shallot is very soft, about 20 to 30 minutes.
4. When the shallot is cool enough to handle, remove the skin and the root end. Puree the shallot and salt in a food processor.
5. Add the mustard and puree. Add the vinegar by the tablespoon, pureeing after each addition.
6. With the motor running, add the olive oil and stock slowly through the feed tube.
7. Stir in the chives and pepper. Adjust the salt and pepper to taste.
For the barbecued chicken and grilled onion:
1. Preheat the grill to medium-high.
2. Brush the chicken breasts and onion slices with olive oil and season with salt and pepper.
3. Grill the chicken for about 4 to 6 minutes each side, depending on the thickness until the chicken is cooked through. During the last 3 minutes of cooking, brush the chicken on all sides with the barbecue sauce. Grill the onion about 2 to 3 minutes per side, using a spatula to turn the onions while being careful to keep the rings together. Remove the chicken and onions from the grill and place on a cutting board to rest. Cut the chicken into strips. Separate the onion slices into rings.
(The chicken and onions can be grilled in advance and stored in the refrigerator for up to 2 days.)
For the spinach salad:
1. Place the lettuce in a bowl and toss it with the vinaigrette. Arrange the chicken strips and grilled onion rings on top.