To make the avocado vinaigrette-put all of the ingredients into a food processor or blender. Mix until smooth.
To make the blue cheese vinaigrette-put all of the ingredients into a food processor or blender. Mix until smooth. If the dressing is too thick, add a drizzle of extra olive oil and mix again.
To make the potatoes-boil a large pot of water and salt well. Boil potatoes until they are fork tender. Drain the water and return potatoes to the pot. Stir in butter, shallot, and parsley. Stir well. Set aside and keep warm until serving.
Grill the chicken and brush each piece liberally with bbq sauce. Cut into strips and set aside.
To plate the salads-place mixed greens on a plate. Lay the sliced chicken on top of the greens. Top with tomatoes, black beans, corn, and fried onions. Place a few warm potatoes on the side. Drizzle entire salad with avocado vinaigrette and blue cheese vinaigrette.