Preheat the oven to 375 degrees F. Spray a mini muffin pan generously with nonstick cooking spray.
Set aside 12 pretty mushrooms slices. Put the rest of the mushrooms slices in a food processor and pulse until ground into small pieces, about 10 seconds. Add the Gorgonzola, flour, breadcrumbs, tarragon, basil, lemon zest, salt, pepper and eggs. Pulse until a thick paste is formed, about 30 seconds more.
Gently roll out the puff pastry to a 10-inch square. Use a 2 1/2-inch round cutter to cut 12 rounds of dough. Poke the rounds with a fork.
Lay 1 reserved mushroom slice in the bottom of each muffin cup. Spoon 1 tablespoon of the cheese mixture over the mushroom in each cup and top with a puff pastry round.
Bake until the puff pastry is golden brown, 25 to 28 minutes. Cool for 2 minutes in the pan before inverting the tartlets. Serve immediately.