With a sharp knife, score the fat of the duck breast in a crisscross pattern, being careful to not cut into the meat. Season the duck with salt and pepper. Warm a cast-iron or heavy-bottomed pan over medium-low heat and add enough oil to just coat the bottom of the pan.
Place the duck breast fat-side down in the skillet to render off the fat, about 8 minutes. Once the fat has rendered out and the skin is golden brown and crisp, turn the duck breast over and add the butter, thyme and garlic. Turn up the heat to medium-high and, once the butter is foamy, begin basting the duck breast using a spoon. Continue basting until the duck breast reaches medium rare and measures 135 to 140 degrees F. on an instant-read thermometer, 2 to 3 minutes. Remove from the pan and let rest for 3 to 4 minutes before slicing.
Pekin duck, also sold as Long Island duck, is known for it's dark, flavorful meat.