In a small bowl, combine the shallots and vinegar. Let sit for 10 minutes. Add the cream and mustard, and whisk to combine. Add the oil in a steady stream and whisk until emulsified. Season to taste with salt and pepper.
Line 4 large plates with the Bibb lettuce leaves.
In a large bowl, combine the lettuces, tomatoes, endive, cheese, ham, and chicken. Add dressing to taste and toss to coat. Arrange the mixture in the center of the Bibb lettuce leaves. Decoratively arrange the egg slices around the outer edges of the greens. If desired, drizzle with more dressing. Garnish with the chives and parsley and serve.