Make the cookie dough:
In the bowl of an electric mixer, beat the butter, brown sugar, and granulated sugar on medium-high speed until very well combined. Add in the egg and vanilla and beat until combined. On low speed gradually add the flour and salt. Stir in the chocolate chips.
Shape the dough into 1-inch balls and place on a parchment lined baking sheet. Refrigerate until firm, at least one hour or up to 2 days if placed in an airtight container.
Prepare the dough for frying:
In a medium bowl, whisk together the flour, baking powder, salt, and sugar. Add the milk and vegetable oil, and whisk until the batter is smooth and free of lumps.
In a medium heavy pot, heat 2 inches of oil until it reaches 360°F. Take a chilled ball of cookie dough and dip it in the batter, turning it over with your hands until it’s completely covered. Let excess batter drip back into the bowl, then gently drop it into the oil. Fry up to 4 or 5 balls at a time.
Fry the balls for about 1 1/2 to 2 minutes per side, or until they’re puffed and a dark golden brown on all sides. Remove them from the oil using a frying skimmer and place them on a paper towel-lined baking sheet to drain. Repeat with the rest of the cookie dough balls and batter. Maintain the temperature of the oil between 360 to 370°F.
Drizzle the balls with melted chocolate and a dusting of powdered sugar before serving warm. These are best served the day they’re fried, but can be kept warm in a 175°F oven until ready to serve.
