Line an ungreased cookie sheet with parchment paper or silpat. Set aside.
In a large bowl using a hand-held mixer or stand mixer with paddle attachment, cream the butter and sugars together on medium speed until fluffy and light in color. Mix in egg and vanilla. Scrape down the sides as needed. On low speed, mix in flour, cornstarch, baking soda and salt. Stir in chocolate covered pretzel pieces. Chill dough (covered) for 1 hour or up to 3 days.
Preheat oven to 350F. Drop balls of dough (2 tablespoons each) onto cookie sheet OR used a standard-sized cookie scoop. Bake for 9-10 minutes, until barely golden brown around the edges. Do NOT cook them longer than 10 minutes. Remove and press down the tops of cookies if they appear too puffy. Let cool for 5-10 minutes on the cookie sheet. Transfer to cooling rack.
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