In a small food processor, pulse kimchi until it’s in a coarse paste. Add butter and pulse until it’s mostly smooth.
Working with chicken thighs, separate skin and rub about a tablespoon of the kimchi butter between the chicken and the skin.
Add chicken thighs skin-side down to a COLD cast iron skillet over medium-low heat. Season chicken thighs with a pinch of salt. Let cook for about 15-20 minutes until fat is rendering out and skin is getting browned. Don’t mess with them while they cook!
When skin is getting browned, flip chicken thighs so the skin is up. Move the skillet to a preheated oven and cook for another 15-20 minutes until chicken thighs are cooked through (185 degrees F. in a thick part).
Remove skillet, add a dollop of kimchi butter to the top of each thigh. Return to oven for 5 minutes.