Preheat your oven to 350°F.
In the bowl of a stand mixer, cream together 1 cup of white sugar, 1 cup of brown sugar, ½ cup of softened butter, and ½ cup of vegetable oil. Mix on medium speed until the mixture is fluffy and light in color, about 2 to 3 minutes.
Add 2 eggs, one at a time, to the butter mixture. Mix well after each addition until the mixture is smooth and creamy.
In a separate bowl, sift together 1 teaspoon of baking powder, 1 teaspoon of salt, 1 teaspoon of baking soda, and 3 cups of all-purpose flour.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined.
Add 1 teaspoon of vanilla extract to the dough and mix until incorporated.
Gently fold in the chopped M&Ms and ½ cup of white chocolate chips.
Scoop the dough and roll it into balls, about 1 to 2 inches in diameter. Place them on a baking sheet lined with parchment paper.
Add 5 whole M&Ms to the top center of each dough ball.
Bake the cookies in the preheated oven for 8 to 9 minutes, or until the edges are lightly golden. Allow the cookies to cool on the sheet for a few minutes before transferring them to a wire rack.