Make small incisions all over the lamb loin and insert the garlic slivers and rosemary sprigs.
Place the meat in a preheated hot griddle pan and cook, turning occasionally, until seared all over for about 10 minutes for rare or about 20 minutes for well done.
Add the onions half-way through the cooking time and char on the outside. Let the lamb rest for 5 minutes, then carve into slices.
Meanwhile, put the oil and rosemary in a mortar and crush with a pestle to release the flavours. Season with salt and pepper.
Spoon the rosemary oil over the lamb slices and serve at once with the fried onions.
Serve with fresh pasta, lightly tossed in oil, and Parmesan shavings.