In a medium pot set over medium-high heat, bring the broth, bay leaves and 1 teaspoon salt to a boil. Lower the heat to medium-low, drop in the tongues and simmer for at least 3 hours. The tongue should give willingly to the point of a sharp knife. If the tongue floats, flip it periodically. Remove from heat.
While the tongues are still warm, transfer them to a cutting surface and peel it with your fingers or a paring knife. The skin is really the only icky thing about tongue: underneath it is pure meat. Slice the peeled tongue thinly and return it to the broth to rest. Turn the heat off the broth and cover.
To prepare the dressing, place the garlic, remaining salt, vinegar and mustard in a food processor or blender. Puree briefly. Then, with the motor running, remove the cap from the center of the blender and drizzle in the olive oil. Buzz this 30 more seconds and move the dressing to something pourable.
Mix the greens in a large bowl and tear them into smallish pieces you can eat with a fork. Toss in a few tablespoons of dressing, just enough to coat. Divide the greens evenly on four plates.
Remove the tongue slices from the broth and toss with some more dressing. (if you have extra dressing, save it for another use) Arrange a few slices of tongue atop each of the plated greens, grind pepper over it and serve.