In a cast iron skillet melt the butter, then sprinkle the sugar over it. Drop the cinnamon stick in the middle then arrange the pears, cut side up in the sugar.
Cook on low heat until the pears start to absorb the caramel and the juices are bubbling around them. I like to cook them slowly and for a while so the pears take on as much caramel as possible. My stove is really intense so I have to move the pears around so they are getting cooked evenly. This usually takes about 30-40 minutes, depending on the size of the pears. If you are using a softer pear it will go much faster. Just keep an eye on them.
Preheat the oven to 350°F (If you are using puff pastry turn the heat up to 375°F).
Once the pears are coloring nicely and the caramel is bubbling turn off the stove and let them cool for about 15 minutes. Sprinkle the pomegranate seeds over the top and drape a circle of dough over the pears. The dough should be about 1″ beyond the edge of the pears. Some doughs, especially puff pastry, will shrink as it bakes, so you want to make sure you have plenty to cover the pears.
Place the entire skillet in the oven and bake for about 30 minutes, or until the dough is nice and golden brown.
Allow the tart to cool in the skillet for about 5 minutes and then invert it onto a serving platter. Make sure the platter is larger than the skillet so that when you flip it all of the hot caramel juices don’t spill out. Needless to say this should be served with something nice and creamy. I served it with unadorned creme fraiche, but vanilla ice cream would be excellent as well.