Preheat the oven to 350° F. Line a baking sheet with parchment paper.Add the butter to a skillet 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 or so.To the browned butter, mix in the brown sugar, 1/3 cup pumpkin butter, the egg, vanilla, and espresso powder, mixing until smooth. Add the flour, oats, baking soda, pumpkin spice, and salt. Dollop the remaining 1/3 cup pumpkin butter over the dough. Sprinkle over the chocolate chips. Gently fold the pumpkin butter and chocolate into the dough, being careful to not over-mix. You want streaks of pumpkin butter. Roll the dough into rounded tablespoon size balls, it might be a little sticky. Place 2 inches apart on the prepared baking sheet. Gently flatten the dough down. Bake 8 minutes. Remove from the oven, rotate, and tap the baking sheet on the counter 1-2 times to flatten. Bake another 2-3 minutes or until the cookies are just beginning to set on the edges.Sprinkle with sea salt (if desired). Let the cookies cool on the baking sheet. They will continue to cook slightly as they sit on the baking sheet.