Thaw the puff pastry according to the package directions.
Preheat the oven to 475 degrees F. Place the puff pastry on a piece of parchment paper on a baking sheet. Fold the edges of the puff pastry over on itself to form a 1/2" border along all four sides of the sheet. With a sharp knife, gently score the puff pastry along the inside edge of the folded over border, and prick the pastry inside the borders with a fork at 1" intervals.
Bake until puffed and golden brown in color, about 8 minutes at sea level; 11 minutes at 6500 feet above sea level.
In a small bowl, combine the cheese and 1 teaspoon of the honey. Mix well with a fork to form a smooth spread. Spread the cheese inside the borders of the puff pastry, and arrange the fig quarters on top. Return to the oven for 5 - 6 minutes at sea level until the cheese is very soft and the rim of the pastry a golden-brown; 8 - 9 minutes at 6500 feet above sea level.
Remove from the oven and sprinkle the thyme over the tart. Tear the proscuitto, if using, into small long pieces and arrange on the tart. Add the arugula.
Drizzle the remaining honey over the tart from the tines of a fork.
Slice with a pizza slicer so there is one fig quarter per piece, and serve.