In a bowl, combine pressed garlic, 3 tablespoons of olive oil, chopped parsley, Tabasco sauce, sea salt, black pepper, and dried thyme. Mix well to form a marinade.
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Place lamb chops in a shallow dish and coat them thoroughly with the marinade. Cover the dish and refrigerate for at least 2 hours, allowing the flavors to infuse.
Preheat your grill to medium-high heat.
Remove lamb chops from the refrigerator and let them come to room temperature for about 30 minutes.
Brush the grill grates with olive oil to prevent sticking.
Grill the lamb chops for about 3-4 minutes per side for medium-rare, adjusting the time based on your preferred doneness.
While the lamb is grilling, prepare the Tabasco glaze. In a small saucepan, heat the chicken or beef stock over medium heat.
Once the stock is simmering, whisk in the softened butter until the sauce is smooth. Allow it to simmer for 3-5 minutes, or until slightly reduced.
Brush the grilled lamb chops generously with the Tabasco glaze during the last few minutes of cooking on each side.
Reserve some glaze for serving.
Once the lamb chops are done, remove them from the grill and let them rest for a few minutes.
Drizzle the remaining Tabasco glaze over the lamb chops before serving.
Sprinkle fresh parsley over the lamb chops for a burst of color and freshness.
Serve the lamb chops hot with additional Tabasco glaze on the side.