Important note about properly measuring flour using measuring cups: The proper way to measure flour using measuring cups is to aerate it first. This is done either by sifting flour, or aerating it by fluffing it up and whisking it well, then spooning it into the measuring cup, then carefully removing any excess flour with a knife. If you just stick that measuring cup in the bag of flour and scoop some out, you will get a lot more flour than what the recipe calls for. Do aerate the flour, or you will end up with dry dough!
Preheat oven to 350 degrees Fahrenheit.
Using an electric mixer, cream peanut butter and butter in a mixing bowl until smooth, about 1 minute. Add brown sugar; beat until combined. Add an egg and vanilla, and continue beating until creamy.
In a separate bowl, combine together flour and baking powder and mix.
Gradually add dry ingredients to wet ingredients, using an electric mixer on low speed.
Prepare baking sheet by lining it with parchment paper. Roll about 2 tablespoons of cookie dough into a ball, rolling each ball between your hands.
Place cookie balls 2 inches apart on a prepared baking sheet. Press white chocolate chips and the M&Ms into the cookie dough balls, about 4 white chocolate chips and 3-4 peanut butter M&Ms per cookie, somewhat flattening the cookies.
Bake for about 12 minutes. Remove from oven and let the cookies cool at least 10 minutes on baking sheet before transferring the cookies to rack or plate to cool completely.