Whisk together flour, cornstarch, baking soda, and salt in a medium bowl.

Combine brown sugar, white sugar, butter, and shortening in a large bowl; beat with an electric mixer until light and fluffy. Mix in egg, vanilla extract, and molasses on low speed. Gradually add flour mixture and blend until just combined. Fold in chocolate chips, cherries, and pecans with a wooden spoon. Cover and place in the refrigerator until well chilled, at least 2 hours.

Preheat the oven to 350 degrees F (175 degrees C). Line 2 cookie sheets with parchment paper or silicone mats.

Roll dough into scant 1/4-cup-sized balls and place 2 inches apart onto baking sheets.

Bake in the preheated oven until golden brown on the edges and slightly underdone in the middles, 12 to 14 minutes. Remove from the oven and sprinkle with sea salt. Cool on the baking sheet for 5 minutes, so cookies can continue to cook, before removing to a wire rack to cool completely.