Position a rack in the lower third of the oven. Preheat the oven to 350° F.Butter an 8-inch pie plate, then sprinkle with 1 tablespoon cinnamon sugar. Fit the pie crust into the pie plate. Brush the edges of the crust with beaten egg, then sprinkle with cinnamon sugar. Lightly prick the bottom of the dough with a fork. Freeze 10 minutes.Meanwhile, add the butter to a small saucepan set over medium heat, cook until the butter begins to brown, about 3-4 minutes. Remove from the heat and transfer to a heatproof bowl. Let cool 5 minutes. Whisk together the brown sugar and 2 eggs, and 1 egg yolk until well combined. Add the cream. Whisk in the warm brown butter and vanilla. Fold in the chocolate caramels and chocolate chips. Pour the mixture into the crust, making sure the chocolate is evenly distributed throughout. Sprinkle the top of the pie with 2-3 tablespoons of cinnamon sugar. Place the pie on a baking sheet. Bake for 40-55 minutes, until the pie is puffed on top, but still wiggly in the center. The longer you bake, the more set your pie will be. I bake between 40-45 minutes. Remove from the oven and let cool 15-20 minutes. Serve the pie warm, sprinkled with sea salt (if desired), and dolloped with whip cream or ice cream. Or serve at room temp. Both options are great!