Make the dressing by placing the mustard in a bowl and add the vinegar. Start beating with a wire whisk and add the oil slowly as you do. Add the pepper.
Divide the dressing evenly between 2 bowls. Put the radiccio leaves int one of the bowls and toss well. Place the Bibb lettuce leaves in the other and toss.
Arrange a ring of radiccio around the outer edge of each plate. Place the Bibb lettuce in the center. Crumble the goat cheese over the lettuce.
Distribute the tomatoes evenly over the goat cheese on each plate.