In the bowl of an electric mixer (or using a hand mixer or elbow grease), combine the butter, brown sugar, and granulated sugar until smooth and creamy. Add the eggs and vanilla, followed by the oats, and beat again just until smooth.
In a small bowl, whisk together the flour, baking powder, baking soda, and sea salt. Sprinkle the dry ingredients over the butter-sugar mixture, and mix on low speed just until combined. Stir in the chocolate chips by hand.
Unwrap caramels and cut each in half using kitchen shears or a sharp knife. Portion out dough scoops of roughly 1/4 cup each, stuff each with 2 caramel pieces, and gently roll into a ball, being certain to completely enclose the caramel inside the dough. Arrange the dough balls on baking sheets prepared with silicone liners or parchment paper, and refrigerate for about 1 hour.
When ready to bake, preheat the oven to 360 degrees F (185 degrees C). Bake cookies for 10-12 minutes, until lightly browned on the edges but still soft in the middle. Garnish with additional sea salt immediately after removing from the oven. Let cool on the baking sheets for 10-15 minutes, until cookies are set, then transfer to wire racks and enjoy.
Notes
If you want to work ahead, or get distracted (what!?), good news - you can chill the dough balls for up to a week! They will bake up slightly browner the longer they have been chilled. I would also like to try experimenting with freezing the dough and baking from frozen, much like these beloved favorites; if you try this, please come back and let us know how it went in the comments!