Preheat the oven to 350 degrees.
In the bowl of an electric mixer, beat together butter and brown sugar on medium high speed until the mixture is creamy and light in color, about 3 minutes. Add the eggs one at a time, beating well after each addition. Mix in vanilla.
Add the flour, oats, baking powder, soda, and salt and beat on low speed until well combined.
Stir in the chocolate chunks and cherries.
Refrigerate the dough for 2 hours or overnight. If you're in a hurry, you can scoop the dough onto baking sheets and freeze for 15 minutes.
To bake, drop heaping Tablespoons of dough onto a parchment lined cookie sheet, about 2 inches apart. Bake for 11-13 minutes or until outsides are golden and interior is still a bit soft and puffy. Dot with a few additional chocolate chunks or cherries for a beautiful presentation. Allow the cookies to set up completely on the cookie sheet and then remove to a wire rack to cool.
Sprinkle with flakes of sea salt and store in an airtight container.