Position racks in the upper and lower thirds of the oven and preheat to 325 degrees F. Line 3 baking sheets with parchment.
Whisk the flour, cocoa and salt together in a medium bowl. Put the butter, unsweetened and semisweet chocolates in a large microwave-safe bowl. Microwave in 30 second increments, stirring until melted, 3 to 4 minutes.
Stir the granulated and light brown sugars into the chocolate mixture until blended and then add the milk, vanilla and eggs and beat vigorously with a wooden spoon or spatula until thick and glossy. Add the flour mixture and stir until just combined. Stir in chocolate chunks and dried cherries.
Drop the batter in heaping tablespoons onto the prepared baking sheets, about 2-inches apart. Bake until the cookies are set on the edges but still soft in the middle, 12 to 15 minutes, rotating the pans halfway through the baking time. Cool on the baking sheets on a wire rack for 5 minutes, then transfer to the wire rack to cool completely.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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