Peel pears, split each in half and remove core (a teaspoon or melon baller works well for this); cut halves in half again, removing any stem and bottom "button." Toss pear quarters very gently in lemon juice. Melt butter in oven-proof skillet with syrup and sugar over med. heat until dissolved 2 min. Add pears, arranging with tips pointing inward. Gently cook over medium heat 20 min, without stirring, until caramel is aromatic and reduced to a deep golden color. Avoid burning the caramel by gently moving the pan back and forth for even heat; reduce heat if bubbling rapidly. Remove from heat and sprinkle with chopped candied ginger and nutmeg.
Meanwhile, cut puff pastry to slightly overhang skillet by 1." Carefully place pastry over pears, tucking in edges with a butter knife to avoid hot caramel burns. Place in preheated 375 degrees oven with a sheet pan underneath to catch any spillover, and bake until very puffed and golden in center, approx. 30 min. Remove from oven and let rest 5 min. With a sharp knife, carefully run tip around edge of skillet to free the tart easily when flipped. Using heavy oven mitts and working over a cleared table, place a rimmed serving plate upside down over skillet/tart. Hold firmly with both hands, pinching each side of pan and platter together; lift quickly and, in one fast motion, flip over and set platter and tart onto work surface with the skillet still on top (now upside-down). Carefully lift skillet away from tart. Let cool to room temperature and serve with crème fraîche, vanilla ice cream or whipped cream, as desired.