Place duck breast skin side-down on a cutting board. Cut a small slit from top to bottom, 2/3 of the way through the duck breast. Season with salt and pepper.
Preheat oven to 400 degrees F (200 degrees C).
Heat a skillet over medium-high heat. Place duck breast skin side-down in the hot skillet; cook until browned, about 30 seconds. Flip and repeat on the other side.
Transfer duck breast to a clean work surface, skin-side down. Place 3 or 4 garlic strips inside the slit. Place rosemary sprig over garlic; top with remaining garlic strips. Place skin side-up in a baking pan.
Bake in the preheated oven until an instant-read thermometer inserted into the center reads 120 degrees F (50 degrees C), about 10 minutes. Cover with aluminum foil. Let rest for 5 minutes before slicing.