Thoroughly pat lamb chops dry with paper towels, wiping away any possible bone fragments or shards. Slice between ribs to separate chops, cutting into 3/4" or 1" thick even portions.
Stir together marinade ingredients in a measuring cup: 5 pressed garlic cloves, 3 Tbsp olive oil, 2 Tbsp parsley, 2 tsp Tabasco, 1 tsp salt, 1 tsp pepper, and 1/4 tsp thyme.
Place lamb chops in a non-reactive casserole dish, pour over the marinade, and rub all sides of lamb chops (focusing on meaty portions) with marinade. Cover and refrigerate for at least 1 hour or overnight.
Remove lamb chops from the refrigerator 30 minutes before cooking. Place a large heavy pan over high heat and add 1 Tbsp oil. Once the oil is hot, add chops and sear for 2-4 minutes per side, depending on the thickness of chops and desired doneness on a thermometer; keep in mind temp rises 5 degrees as it rests. Sauté in 2 batches if needed. Transfer to a serving plate, tent with foil, and rest for 5 minutes while making the pan sauce.
Spoon out excess oil from the pan (leave in 1 to 2 Tbsp oil), being careful not to remove the drippings and flavorings.
Add 1/2 cup stock and simmer 2 min. Turn off heat then swirl in 2 Tbsp softened butter, 1 tablespoon at a time. Spoon sauce over lamb chops and garnish with more parsley if desired.