Remove the pork chops from the refrigerator and allow them to come to room temperature for 20 minutes.

Pat both sides of the pork chops dry with paper towels, then season generously with kosher salt and freshly ground black pepper.

Preheat a 12-inch cast iron skillet or heavy-bottomed pan over medium-high heat for 2-3 minutes until hot.

Add olive oil to the pan, swirl to coat, and place the pork chops in the pan. Sear undisturbed for 4-5 minutes until a deep golden crust forms.

Flip the pork chops using tongs and cook the second side undisturbed for 3-4 minutes.

Reduce heat to medium, add butter, smashed garlic, and thyme to the pan. Tilt the pan and baste the pork chops with melted butter for 1-2 minutes.

Insert a meat thermometer into the thickest part of a pork chop (not touching the bone) and cook until the internal temperature reaches 145°F.

Transfer the pork chops to a warm plate and let rest for 3-5 minutes. Add white wine or chicken stock to the pan, scraping up browned bits to create a pan sauce.

Chill martini glasses in the freezer or fill with ice water. In a cocktail shaker, combine gin, dry vermouth, olive brine, and ice. Stir gently for 10-15 seconds until well chilled.

Strain the martini into chilled glasses, garnish with green olives and a lemon twist. Plate the rested pork chops, spoon the pan sauce over them, and serve immediately alongside the martini.