Beat butter, brown sugar, and granulated sugar with a heavy-duty electric stand mixer on medium-high speed until light and fluffy, about 3 minutes. Add eggs, 1 at a time; beat until well combined after each addition. Beat until fluffy, about 1 minute. Beat in vanilla. Stir together flour, oats, baking powder, and baking soda in a small bowl. Gradually add to butter mixture, beating until well blended. Stir in chocolate chunks and chocolate chips.

Using a 3-tablespoon scoop, drop spoonfuls of dough onto parchment parchment paper-lined baking sheets 2 inches apart. Chill 24 hours.

Preheat oven to 375°F. Bake cookies in preheated oven until edges are golden and bottoms are set, but cookies are still very soft to the touch, 11 to 13 minutes.

Remove cookies from oven, and sprinkle evenly with salt; cool on baking sheets on wire racks 5 minutes. Serve warm, or transfer cookies to wire racks to cool completely, about 20 minutes.