Dry the chops with paper towels, and season aggressively with salt and pepper. Swirl the olive oil into a large skillet, and heat over medium until the oil begins to shimmer. Add chops, and cook until well browned on each side and cooked through, about 5 minutes per side. Transfer chops to a plate, and cover to keep warm.

Drain the fat from the skillet, then melt 2 Tbsp of butter in it over medium heat until sizzling. Add the shallot and garlic, and sauté until the aromatics soften, reducing the heat if necessary, about 1 minute. Sprinkle in the flour, and cook, stirring, about 2 minutes. Whisk in the wine and chicken stock, raise heat to high and bring the liquid to a boil, scraping up the browned bits on the bottom of the pan. Reduce the heat to medium-high and cook, uncovered until the liquid is reduced by half, 7 to 10 minutes.

Stir in capers, basil, lemon zest and juice. Simmer for 1 to 2 minutes. Stir in the remaining 2 Tbsp of butter until it is melted and the sauce looks smooth. Nestle the pork chops into the sauce, and allow them to warm up for a couple of minutes, then serve, pouring sauce over each pork chop to taste. Garnish with fresh basil.