Step 1

Season pork chops with salt and sprinkle evenly with ½ tsp. sugar. Heat 1 Tbsp. oil in a large skillet over medium-high. Cook chops, undisturbed, until well browned underneath, about 3 minutes. Turn and cook just until second side is lightly browned, about 1 minute. Transfer chops to a plate (they won’t be fully cooked); reduce heat to medium.

Step 2

Pour remaining 1 Tbsp. oil into same skillet and add shallot and garlic. Cook, stirring often, until softened and just beginning to brown, about 3 minutes.

Step 3

Add vinegar and remaining 1 tsp. sugar to skillet. Cook, swirling pan occasionally, until vinegar is nearly evaporated, about 2 minutes.

Step 4

Add rosemary, capers, and ½ cup water to skillet; season with salt. Reduce heat as needed to maintain a very low simmer. Add butter and swirl pan continuously (and vigorously) until sauce becomes smooth, glossy, and emulsified.

Step 5

Return pork chops to skillet, arranging darker side up. Simmer gently in sauce, swirling occasionally, until chops are cooked through, about 3 minutes (a thermometer inserted near the bones should register 135°).

Step 6

Transfer pork chops to plates and spoon sauce over.