Pour the oil into a large frying pan and fry the mushrooms over medium-high heat for about 5 minutes, until browned.
Add the shallot and garlic, then continue cooking for about 2 minutes. Deglaze with the cider vinegar, and add the tarragon, fleur de sel and pepper.
Remove from heat and reserve.
Preheat the oven to 190°C.
On a baking tray, place the 4 slices of bread, spread them with the olive pulp and mushrooms, and divide the mushrooms and cheese into 4 equal parts.
Grill for about 8 minutes or until the cheese is melted and the bread is toasted.
Remove from the oven and add the garnish to each slice of bread: a little parsley, 1 pinch of salt, 1 turn of the pepper mill.
Serve the toast hot or cold.