Begin by preheating your oven to 350°F (175°C). In a large mixing bowl, cream together the butter and both sugars until the mixture becomes light, fluffy, and airy—this should take about 2-3 minutes. Next, add in the peanut butter, ensuring it's fully incorporated into the mixture. Follow with the egg and vanilla extract, mixing until the batter is smooth.
In a separate bowl, combine the flour, oats, salt, baking powder, and baking soda. Be sure to measure the flour correctly by spooning it into your measuring cup and leveling it off before adding it to the mix. Gradually fold this dry mixture into the wet ingredients, blending until just combined.
Gently stir in the chocolate chips and M&M candies, distributing them evenly throughout the dough. Use a 1-inch cookie scoop to portion the dough onto a baking sheet. If you prefer larger cookies, adjust the baking time accordingly, but generally, bake them for 10-12 minutes. The cookies should appear just set when you remove them from the oven—be careful not to overbake.
Allow the cookies to cool completely on the baking sheet before transferring them to a wire rack or serving plate.