Preheat the oven to 350°F. Line a baking sheet with parchment paper and set aside.
Pat the maraschino cherries dry with paper towels and chop them. Set the cherries aside to make sure they are as dry as possible before mixing.
In a medium bowl, whisk together the 2 cups + 2 tablespoons all-purpose flour, ½ teaspoon baking soda, and ½ teaspoon kosher salt.
In the bowl of an electric mixer, beat the 1 ½ sticks (12 tablespoons) softened salted butter, 1 cup brown sugar, and ½ cup sugar on medium speed until light and fluffy, about 4–5 minutes.
Beat in the 1 egg and then the 1 egg yolk until combined. Add the 2 teaspoons vanilla extract and mix until incorporated.
With the mixer on low speed, add the dry ingredients and mix just until combined; do not overmix.
Fold in the 1 cup semi-sweet chocolate chips and the chopped maraschino cherries with a spatula until evenly distributed.
Scoop or roll the dough into balls measuring about 1½ to 2 tablespoons each (a small cookie scoop or two tablespoons works well). Place the dough balls on the prepared baking sheet about 2 inches apart.
Bake for 10 to 12 minutes, until the edges are set and the centers are still slightly soft (cookies will continue to firm as they cool).
Immediately after removing the cookies from the oven, sprinkle with flaked salt. Let the cookies cool on the baking sheet for about 5 minutes, then transfer them to a wire rack to cool completely before serving.