Trim drumsticks if necessary, then season them with sea salt. Preheat oven to 400 degrees.
Heat olive oil in a 12" cast iron skillet over medium heat until shimmering, then swirl in the pan to coat. Brown drumsticks on both sides (3-4 minutes per side), then remove the chicken to a separate plate.
While drumsticks are browning, chop your veggies and drain the corn and black beans.
After the chicken is browned, add the onion to the same pan (without wiping out the skillet) and saute over medium heat for two minutes, stirring occasionally.
Stir in the garlic and peppers and continue to cook over medium heat, stirring occasionally, for another five minutes. Stir in the corn and black beans, and season everything with chili powder, cumin, smoked paprika, and cayenne.
Saute the veggies over medium heat for another three minutes, then nestle the browned drumsticks back into the skillet.
Turn off the heat under the pan, and top everything evenly with shredded cheddar.
Move the entire skillet into the oven. Bake at 400 degrees for 25 minutes, or until chicken is cooked through to temperature.
Top your chicken drumsticks Southwest skillet with chopped green onions or cilantro (optional) and serve with salsa and/or sour cream, if desired.
Notes
You could kick things up a notch here by using pepper-jack cheese rather than cheddar, if you prefer a little extra kick.