Remove the stems from the mushrooms and discard. Slice the caps into 1/8 inch slices. Shiitakes are generally very clean and may need only a slight brushing off.
Heat a heavy pan till very hot, cast iron if possible and add 1/4 inch of the olive oil. Add the mushrooms and cook for 15 seconds. Salt and pepper to taste while they are cooking. Add the garlic and shallots but keep stirring the mushroom so that the garlic and shallots do not color or burn.
After 1 minute add the stock and then the cold butter. Swirl the pan to allow the liquid to absorb the butter. This will thicken the sauce.
Pour vinegar in a mixing bowl, add salt and pepper. Whisk in olive oil and adjust to taste. Toss babymixedlettuces in vinaigrette, arrange on plate. Place on top of mixed lettuces a portion of shiitakes. Arrange the diced tomatoes around the shiitake mushrooms.