Preheat the oven to 350°F (175°C). Line a 13x9-inch baking pan with parchment paper, leaving an overhang for easy removal.
In a medium bowl, whisk together the flour, oats, baking powder, baking soda, and 1/2 teaspoon fine sea salt until evenly combined; set aside.
In a large bowl, stir the melted butter, packed brown sugar, and creamy peanut butter until smooth. Whisk in the eggs and vanilla until fully incorporated.
Fold the dry ingredients into the wet mixture until just combined. Then gently fold in the semisweet chocolate chips, peanut butter chips, and mini peanut butter cups, reserving a few tablespoons of each to sprinkle on top if desired.
Press the dough evenly into the prepared pan. Scatter the reserved chips and mini cups over the top, then lightly sprinkle with flake sea salt.
Bake for 25 to 28 minutes, or until the edges are lightly browned and the center is just set; avoid overbaking.
Remove from the oven and cool the bars completely in the pan. Use the parchment overhang to lift the slab out, then slice into squares, rectangles, or triangles to serve.