In a 10-inch cast-iron skillet over medium heat, combine butter, honey, and sugars. Bring to a boil; let boil for 4 minutes. Add pecans and heavy cream, and boil 3 minutes more. Remove from heat, and set aside. Let stand about 30 minutes to cool. Using a wooden spoon, gently mound pecans and caramel slightly in center of skillet, leaving a gap between pecans and edge of skillet.
Preheat the oven to 425 degrees.with rack in the top third. On a clean, lightly floured work surface, roll out one disk of prepared chilled pastry to approximately a 7/8-inch-thick, 13-inch-diameter circle. Place the pastry over the skillet, carefully tucking the dough down against the edge of the skillet and around the edges of the mound of pecans. Trim the excess dough.
Place two rimmed baking sheets, one on top of the other, underneath the skillet to catch any drips while the pie bakes and to provide insulation for the caramel. Place skillet in the oven, and bake pie until the dough is just turning golden brown, about 10 minutes. Reduce heat to 350 degrees, and continue baking until the pastry is cooked through and the caramel is bubbling up around the edges of the skillet, about 30 minutes more.
Remove the pie from the oven, and let cool about 20 minutes. Carefully invert the pie onto a parchment-lined tray or baking sheet (the pie is easy to transfer to serving plate once it has been inverted). Be careful inverting pie; the caramel is very hot. If the pie does not release easily from skillet, heat the skillet over medium heat for about 30 seconds. Serve warm.