In mixer, cream together butter, sugars, and vanilla extract.
Sprinkle in salt and mix.
Stir in flour, gradually.
Add milk and stir until well combined.
Stir in chocolate chips.
Roll cookie dough into 1 1/2 tsp-sized balls and place on wax-paper lined cookie sheet. Place in the freezer while you prepare your donut dough.
Follow directions in Fried Donut Holes Recipe to step 4 (forming dough into cohesive ball).
Transfer dough to a lightly floured surface and roll it out to about 1/8" thickness.
Use a biscuit cutter to cut dough into 2 1/2" circles.
Remove your cookie dough from the freezer and wrap dough around donut holes, tightly sealing inside.
Fill a medium-sized saucepan 2-inches deep with your oil over medium-high heat. Use a candy thermometer (make sure it isn't touching the bottom of the pot) to monitor your temperature.
Heat oil to 350F (you will have to monitor the heat pretty regularly and may need to increase/decrease your stove temperature to keep it consistent).
While your oil is heating, prepare your chocolate sugar mix by stirring together sugar, cocoa, and sea salt in a small dish. Set aside.
Prepare two plates for your cooked donut holes by lining them generously with paper towels.
Gently lower donut holes into oil using a slotted spoon, about 3-4 at a time, and fry for 2-3 minutes (see note)
Transfer to paper-towel lined plate, allow to cool for about 1 minute, and then roll in sugar mixture.
Allow to cool for at least 5-10 minutes (be careful, the cookie dough will be hot!) before enjoying.
*For best results, fry only one donut hole the first time you try this, and gauge how thoroughly it is cooked. After 2 minutes has passed, cut into it to check whether the donut dough is underdone, just right, or overdone, (the cookie dough shouldn't be cooked, it should be gooey) and then fry the rest of your donut holes accordingly. While these should take about 2 minutes under optimal conditions with a consistent oil temperature of 350F, it's still important to check so that you don't end up with 1½ dozen donuts that are still gooey in the middle!