Gather all of your ingredients before you begin. Make sure the butter and eggs are at room temperature so they incorporate smoothly. Line a baking sheet with parchment paper and set aside.
In a stand mixer fitted with a paddle attachment, or using a hand mixer, cream together the butter, granulated sugar, and brown sugar on low speed. Increase to medium and beat for about 5 minutes, until the mixture is light and fluffy. Scrape down the sides of the bowl halfway through mixing.
Add the vanilla bean paste or vanilla extract. Mix in the egg and egg yolk one at a time, beating until fully incorporated.
In a separate bowl, whisk together the all-purpose flour, bread flour, salt, and baking soda. Gradually add the dry ingredients to the wet ingredients, mixing just until combined. Avoid overmixing, as this can create a tough cookie. Gently fold in the M&M candies until evenly distributed throughout the dough.
For deeper flavor and a chewier texture, refrigerate the dough overnight or up to 72 hours. If you are short on time, the dough can be baked immediately.
Preheat the oven to 325°F (163°C). Scoop about 2 tablespoons of dough per cookie onto the prepared baking sheet, spacing them a few inches apart. Bake for 15 to 20 minutes, until the edges are golden brown and the centers remain soft.
Allow the cookies to rest on the baking sheet for 5 minutes before transferring them to aluminum foil to cool completely. Cooling on foil instead of a wire rack helps maintain soft centers.