Place the butter, honey, and both sugars in a 10" cast-iron skillet set over medium-low heat. Stir until the ingredients are melted and bring the mixture to a boil. Boil for 5 minutes, stirring often. Add the pecans, heavy cream, and vanilla, and boil for 3 more minutes. Remove the pan from the heat. Set aside and cool for 20 minutes.
Position an oven rack on the middle level and preheat the oven to 400°F. Roll out the refrigerated pie dough over the skillet, pressing down against the pecan filling. Fold in the edges of the pie dough, about 1/4", and press to seal it. Cut a 1-1/2" slit in the middle of the pie.
Place the skillet on a metal baking sheet and bake for 15 minutes. Reduce the oven temperature to 350°F, and continue baking for 13–15 more minutes, or until golden brown and the caramel is bubbling around the edges of the skillet. Remove the pie from the oven, and let it cool about 15 minutes.
Carefully invert the pie onto a serving plate. (If there are any pecans that stick to the skillet, just scrape them off with a spatula and place them on top of the other pecans.) Let the pie cool for 15 minutes. Pour the melted chocolate chips into a piping bag and draw stripes on top of the pie. (Or, just drizzle on the chocolate with a spoon.) Cut and serve warm.