Preheat oven to 350F. Line two baking sheets with parchment paper. In a medium bowl, whisk together flour, oats, baking soda, cinnamon, and salt until well combined.

In a large bowl, beat softened butter with brown sugar and granulated sugar on medium speed until light and fluffy, about 3 minutes. Scrape down the bowl as needed. Beat in the egg and vanilla until fully incorporated, about 1 minute more.

Add the dry ingredients to the butter mixture and mix on low speed just until no flour streaks remain. The dough will be thick and slightly sticky.

Using a rubber spatula, gently fold in the diced apple and caramel pieces until evenly distributed throughout the dough. Try to distribute the caramels so they don't clump together.

Using a 2-tablespoon cookie scoop or heaping tablespoon, drop dough onto prepared baking sheets, spacing 2 inches apart. Press gently to flatten slightly. Bake until edges are golden brown and centers look set, 12 to 14 minutes. The caramel may bubble up and create small pools - this is normal and delicious.

Let cookies rest on the baking sheet for 5 minutes - they will be quite soft at first. Transfer to a wire rack to cool completely. While still warm, sprinkle lightly with coarse sea salt if desired. Cool completely before storing so the caramel firms up.