Place the bowl of a stand mixer (or a standard mixing bowl) in the freezer.
To prepare the edible cookie dough, place the flour in a microwave-safe bowl and microwave for 1 minute, stirring every 15 seconds. Check that the internal temperature reaches 165 F.
Stir the butter, granulated sugar, brown sugar, vanilla, and salt to combine in a small bowl.
Add the flour and milk and stir until thick but uniform.
Fold in the mini chocolate chips.
Roll a few mini balls of cookie dough in your hands and transfer them to a separate bowl for the topping.
To prepare the blizzards, beat the ice cream on low speed in the chilled mixing bowl, sprinkling in half of the remaining cookie dough, until the ice cream softens and sticks to the edges of the bowl.
Add the chocolate chips, remaining cookie dough, and Nutella, and beat for a few seconds on low to combine.
Spoon the ice cream into glasses and smooth the tops with a spoon.