Bring a large pot of water to boil over high heat and add chicken drumsticks, poaching them until no longer pink, around 5 minutes. Drain, rinse the chicken under cold tap water, return to empty pot.
In a small bowl, stir the soy sauce, gochugaru, gochujang, brown sugar, garlic, 1 1/3 cups water and add to the pot. Bring to a boil over high heat. Reduce the heat to medium and cook at a gentle boil until the sauce has reduced slightly about 10 minutes.
Add the onion, potatoes, carrot, jalapeno and continue gently boiling until the chicken is tender and no longer pink, 20-30 minutes.
Stir in the sesame oil and garnish with sliced scallions.
Serve the pot of Dakdoritang with steamed rice.