Preheat oven to 350 degrees. Using a towel, grasp an oyster in the palm of your hand. Press the oyster, rounded side down, on a firm surface, still holding it with the towel. Shuck the oyster by wedging the tip of an oyster knife (regular knives are too thinbladed) between the halves of the shell, at the shell's narrowest end. When the knife tip is securely wedged, rotate the blade to pry open the shell. Slide the knife blade along the length of the shell to open completely. Remove the oyster from the shell and reserve, along with its juice. From each pair of oyster shells, save the one that is most concave on the inside, and discard the one that is flatter. Place the concave shells in a pan of cold water and scrub inside and out. Place the clean oyster shells on a cookie sheet and set aside.
Dip the tomatoes briefly in boiling water to loosen the skins, then in ice water. Peel, cut in half, remove and discard the seeds and dice.
Lay out the phyllo dough one sheet at a time on a clean work surface. Brush the sheet lightly with olive oil, sprinkle with coarse salt, crumble the sheet like a piece of newspaper and place on a cookie sheet. Bake at 350 degrees for 10 to 12 minutes until golden brown.
Have the sauce ingredients measured and ready beside the stove. When you are ready to begin cooking the oysters, place the cookie sheet containing the oyster shells in a 350 degree oven. On the top of the stove, melt the butter in a hot saute pan until it begins to foam. Add the shallots, the oysters and their juice, and the white wine. Cook the oysters for 30 seconds, then add the heavy cream. Bring to a quick boil, then reduce to a simmer for just a minute more, or until the oysters' edges begin to curl. Add the tomato, tarragon, and bacon. Heat for another 30 seconds, then remove promptly from the heat.
Remove the oyster shells from the oven and arrange six on each plate. Spoon an oyster into each shell and spoon a little of the sauce over each. Top each dish with top hat of crispy phyllo.