Preheat the oven to 425 degrees F (220 degrees C).

Trim silver skin from pork tenderloins; pat dry using paper towels. Rub 2 teaspoons vegetable oil over tenderloins, then rub with sea salt.

Heat 1 tablespoon vegetable oil in a large, oven-proof skillet over medium heat until it shimmers. Cook tenderloins in hot oil, rotating to brown all sides, about 10 minutes. Transfer pork to a large plate.

Add remaining 1 tablespoon vegetable oil to any drippings in the skillet. Cook apples and onions in hot oil, stirring occasionally, until onions turn translucent, about 5 minutes; add more oil if the skillet gets dry. Season with 1 teaspoon thyme and black pepper; stir gently to combine. Remove from heat.

Use a pastry brush to spread Dijon mustard evenly over tenderloins. Sprinkle with remaining 2 teaspoons thyme. Nestle tenderloins into the skillet with apple mixture.

Roast, uncovered, in the preheated oven until an instant-read thermometer inserted into the center of tenderloins reads at least 145 degrees F (63 degrees C), about 15 minutes. Remove the skillet from the oven and transfer pork to a large platter. Cover with aluminum foil and let rest.

Pour chicken stock into a saucepan and cook over medium-high heat until reduced by half, 8 to 10 minutes. Pour into the skillet with apple mixture. Cook over medium-high heat until boiling, about 5 minutes; stir in butter until melted.