Preheat oven to 375° Fahrenheit. Adjust oven racks as needed so that skillet sits in center of oven.
Place chicken thighs on cutting board. Pat chicken completely dry on all sides with paper towels. Liberally season chicken with sea salt, then flip chicken over and salt other side. Set chicken aside.
Heat skillet over medium-high heat. When pan is very hot, add oil and swirl pan to distribute oil evenly across pan surface. Continue heating pan until oil is hot and shimmery.
When oil is hot, place chicken thighs in skillet skin-side down. Sear chicken thighs 7 to 8 minutes or until skin is golden brown and releases easily from pan. If skin sticks to pan, continue searing until skins release easily.
Flip chicken thighs over, then immediately place skillet in preheated oven. Roast chicken thighs 15 minutes, or until internal temperature of chicken reaches 162° to 163° Fahrenheit. Note: skillet will be very hot. Always use potholder when moving skillet or checking chicken temperature.
Once temperature is reached, carefully remove skillet from oven. Transfer chicken thighs to plate and set aside.
Discard all but 2 tablespoons chicken fat from skillet, then return skillet to heat. Reduce heat to medium-low.
Allow skillet to cool slightly, then add minced shallots. Sauté shallots, stirring frequently, approximately 2 to 3 minutes or until softened.
When shallots have softened, add white wine to deglaze skillet. Stir to incorporate wine, making sure to scrape up any browned bits of chicken that might be stuck to bottom of skillet.
Increase heat under skillet to medium-high. Allow mixture to boil until liquid is reduced by 50%.
Add chicken stock to skillet and bring liquid to boil again. Boil mixture until liquid has reduced by 50%. Mixture should be slightly thick, resembling sauce rather than soup.
Stir in fresh herbs of choice, then remove skillet from heat. Allow mixture to cool slightly, then add butter and whisk until butter is completely melted. Taste sauce and add salt as desired.
Plate chicken thighs with sides of choice. Ladle butter sauce over chicken thighs and serve immediately.