Preheat the oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a large mixing bowl, using an electric mixer, cream together the softened butter, peanut butter, light brown sugar, and granulated sugar until light and fluffy, about 3 to 4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract until combined.
In a separate medium bowl, whisk together the rolled oats, all-purpose flour, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.
Fold in the semisweet chocolate chips and candy-coated chocolate pieces using a spatula until evenly distributed.
Transfer the cookie dough into the prepared baking pan and press it down evenly with a spatula.
Bake for 18 to 20 minutes, or until the edges are golden and a toothpick inserted into the center comes out with a few moist crumbs.
Remove the pan from the oven and allow the bars to cool completely in the pan on a wire rack.
Once cooled, use the parchment paper overhang to lift the bars out of the pan. Cut into 24 squares and serve.