Step 11. Heat the oven to 350 degrees and select the serving glasses for the dish. To select the serving glasses, set aside four small glasses or dishes with a relatively narrow diameter (about 1½ inches) and relatively straight sides, such as a whiskey glass or liqueur glass. Chill the glasses before assembling the final dish.
Step 22. Use a bread knife to cut the bread evenly into slices three-sixteenths of an inch thick. Choose a cookie cutter or ring punch that is slightly smaller than that of the interior diameter of the serving glasses. Punch out two disks of bread per portion (e.g., 8 disks for four servings) from the slices of bread. It is a good idea to do a couple of extra so that you can choose the nicest ones.
Step 33. Line a flat, heavy cookie sheet with a Silpat or parchment paper. Brush the Silpat or parchment with a thin film of clarified butter. Evenly distribute the disks of bread on top of the buttered baking mat. Brush another Silpat or sheet of parchment as before and lay this over the disks of bread. Now set another flat and heavy baking sheet on top to sandwich the bread in between.
Step 44. Place the sheet in the center rack of the oven, then place a couple of heavy pans on top of the upper sheet pan. The heavier the better, as this will compress the bread to create a wafer-thin, crispy Melba toast. Toast the bread for 20 minutes, then check and remove any toasts that are golden brown. Continue to bake the remaining toasts, checking every 5 minutes, until all of the toasts are baked (usually about 30 minutes total baking time). Store the toasts in a dry, air-tight container until needed.
Step 55. Prepare the avocado tartare no more than 2 hours before serving to prevent browning. To make the tartare, cut the avocado in half and remove the pit. Scoop the avocado out of the skin with a large spoon, and then finely chop the halves with a sharp knife. Transfer the avocado to a small bowl and mix in the lime juice, salt and ascorbic acid if using, followed by the crème fraîche, olive oil, shallot and zest. Place this mixture into a plastic piping bag, press out as much air as possible and chill it in the refrigerator.
Step 66. About 15 minutes before serving, cut a one-half-inch opening from the tip of the piping bag. Pipe about 3 to 4 tablespoons of the avocado tartare into the bottom of a serving glass. Set two Melba toasts on top of the avocado and gently press to flatten and level the surface as well as expel any air. Next, use a small spoon to place about an ounce of caviar on top of the Melba toast. Use this spoon to carefully flatten and level the surface of the caviar. Repeat with the remaining glasses and serve immediately.