Season the chops with salt, pepper, and sugar.
Heat the oil and butter in a sauté pan and cook the chops on both sides until brown and cooked through, about five minutes per side.
When the chops are done, slide them onto a plate.
Cover to keep warm.
Add the shallot to the pan and fry to soften, about three minutes.
Deglaze the pan with the stock, scrapping up the good sticky bits from the bottom.
Boil down to about 2 tablespoons.
Add the capers, thyme or parsley, and lemon zest, 1 minute.
Add a squirt of lemon juice to taste.
Check the seasonings.
Dribble the sauce over the chops, and serve.