Preheat the oven to 350°F (175°C). Grease or line a 9x13-inch baking pan with parchment paper.
In a large bowl, whisk together the melted butter, brown sugar, and granulated sugar until smooth. Add eggs and vanilla extract, mixing until well combined.
In a separate bowl, whisk together the flour, baking soda, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined. Avoid overmixing.
Fold in ¾ cup of M&Ms and the white chocolate chips, reserving the remaining M&Ms for topping.
Spread the dough evenly into the prepared pan. Sprinkle the reserved M&Ms over the top and press them lightly into the surface.
Bake for 25–30 minutes, or until the edges are golden and a toothpick inserted in the center comes out clean.
Allow the bars to cool completely in the pan. Once cooled, slice into squares or rectangles and serve.