Preheat the oven to 350°F and line a large baking sheet with parchment paper and set aside. If you only have a 9x13-inch baking sheet, you'll want to use two baking sheets for two batches.
In a medium bowl, whisk together 1¾ cups all-purpose flour, ½ cup unsweetened cocoa powder, 1 (3.4oz) box instant chocolate fudge pudding mix, 2 tablespoons powdered milk, ½ teaspoon salt, and ¼ teaspoon baking soda. Set aside.
Add together 1 cup granulated sugar and ½ cup salted butter to a large bowl or stand mixer fitted with a paddle attachment and cream for 1 minute.
Add in 1 large egg and beat until combined. Beat in 1 additional large egg yolk, 2 ounces whole milk, and 1½ teaspoons pure vanilla extract and mix just until combined.
Add half of the dry ingredients to the wet ingredients and beat just until incorporated. Then add the remaining dry ingredients and mix until thoroughly combined.
Scoop the dough with a #24 cookie scoop into 16 2-ounce portions. Gently press the dough flat and then shape it into a bowl shape. Place a heaping teaspoon of the ½ cup hot fudge sauce (about .2 ounces) in the well (or a heaping tablespoon in 4-ounce portions of dough if making larger cookies). Do not heat up the hot fudge first.
Then gently use your hands to fold and work the dough up and around the sides and top of the hot fudge sauce. Pat and pinch the dough to seal it and roll it between your palms to make a smooth ball.
Place the cookies on the baking sheet, usually with the sealed side down. Place cookie dough at least 2 inches apart for regular cookies or 4 inches apart for large cookies on the prepared baking sheet.
Bake for 8 to 10 minutes for regular cookies or 10 to 12 for large cookies until the edges are just set and the top has a matte look. The cookies will look slightly underdone; this is normal as they will continue to cook as they cool.
Allow the cookies to cool on the pan for 15 minutes before transferring them to a wire rack with a spatula to cool completely. These cookies are very soft right after baking and will firm up while they cool.
Dust with powdered sugar while warm.