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Preheat oven to 350F. Line 2 baking sheets with parchment paper.
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Sift together flour and baking soda; set aside.
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In the bowl of a stand mixer fitted with a paddle attachment, cream together butter and sugars until light and fluffy. Add in pudding mix and beat until well blended. Add eggs and vanilla.
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Add flour mixture slowly until well incorporated. Use a rubber spatula to fold in chocolate chips and M&Ms.
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Take heaping tablespoonfuls of dough, roll into balls, and place on prepared baking sheets, leaving about 2 inches space between each one.
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Bake at 350F for 8-12 minutes, rotating sheets halfway through, until light golden brown. Let cool on baking sheet for about 3 minutes before transferring to a wire rack to cool completely. Repeat with remaining dough.