Whisk together soy sauce, water, rice vinegar, liquid smoke, garlic, ginger, white pepper, onion powder, and sesame oil. Place baby carrots into container/bowl with lid, top with liquid (so most of the carrots are fully submerged), cover, and let marinate in the fridge for 12-24 hours.
Once the carrots have marinated, place both the liquid and carrots into a saucepan and bring to a boil. Boil for 14-16 minutes until tender. Drain liquid and place carrots on a towel to absorb any excess liquid and to cool.
Stir together cornmeal, flour, sugar, baking powder, salt, milk, and egg until combined. Pour into a tall glass for dipping.
Heat a dutch oven or stock pot with approximately 2 cups of oil until it reaches approximately 375°F (it will look like it's shimmering). Meanwhile, holding a baby carrot in one hand, gently press the end of one lollipop stick into the carrot, approximately 2/3 of the way inside.
Dip carrots into the glass of cornmeal batter, letting the excess drip off. Place directly into oil (the lollipop sticks can be submerged in the oil too), let cook until golden brown, turning as needed, for 4-5 minutes. Be sure to turn down the heat on your stove, as the oil will continue to get hotter and hotter; you may only need to fry them for 2-3 minutes if the oil becomes too hot. Don't crowd the pan; I fry about 4-6 at a time with the pot I use.
Remove from oil, place on paper towel or cooling rack for excess oil to drain. Serve immediately with condiment of choice.
Notes
Leftovers? Store in an airtight container in the fridge. Reheat in a 375°F oven, preferably on a pizza stone to ensure crispiness. Best reheated 1-2 days after first making.