In a small bowl, stir together mustard, sour cream, ginger, thyme, and a pinch of salt; set aside.
Make several 1/4" slits in pork loin. Slip garlic into slits. Brush loin with oil and season with salt and pepper.
Heat a large cast iron or ovenproof skillet over high heat. Add pork loin and brown on all sides, about 5 minutes. Remove the pan from the heat.
Spread mustard mixture over pork, then transfer the skillet to the oven and cook until a meat thermometer inserted into center of pork registers 150, about 30 minutes. Remove the pan from the oven and transfer pork to a cutting board; loosely cover with foil and let rest for 5 minutes before slicing. Serve warm or at room temperature.