Mix all the ingredients except the avocados in a bowl with a wire whisk. Let this sit for about an hour before moving on.
Slice the avocados in half, remove the pits, then scrape out the contents with a spoon. Avoid any stringy parts at the stem end. Add the avocado to the other ingredients and mash it in with the whisk. Add 1/4 cup cold water, and whisk until smooth. Add a little more water to thin the texture as desired.
Right before serving, toss greens (red and green leaf, romaine, Boston, or Bibb lettuces recommended; watercress makes a nice accent) with the dressing. Garnish individual salads with thin slices of avocado and tomato.