In a pot of boiling water dip mint leaves in for 5 seconds. Remove. Shock in a bath of ice water. Squeeze in a towel to dry. In a blender combine olives with basil, mint, grated parmesan cheese, 1 garlic clove, 4 tablespoons of olive oil, pine nuts, and lemon juice. Pulse puree in blender, achieving course consistency. Season with salt and pepper. Set aside.
Preheat oven to 350 degrees. Cut 1 cup of potatoes length wide in half and place in mixing bowl. Add 1 glove chopped garlic, 1/2 shallot, 1 sprig rosemary chopped, 2 sprigs thyme (leaves only), 2 tablespoons olive oil, season liberally with kosher salt and fresh ground pepper. Line baking sheet with foil. Place potatoes cut side down on baking sheet. Bake for 15 minutes. Flip potatoes over and bake for an addition 15 minutes until golden brown and tender. Add into a small mixing bowl 1 teaspoon of butter and potatoes, mix until butter is melted.
Preheat cleaned and oiled grill on high heat. Season all sides of lamb t-bone liberally with salt and pepper. Place lamb t-bone on grill with top of the steak pointing at 10 o’clock. Let grill mark set for 3 minutes. Turn steak to 2 o’clock for another 3 minutes. Flip steak and repeat. As steak is reaching desired temperature place one sprig rosemary, 2 sprigs thyme, 2 tablespoons of butter atop the steak. Turn off the grill until butter is melted.
Choose your preference of serving steak as is, or sliced off the bone. Drizzle 2 tablespoons of mint pesto. Serve with warm roasted potatoes.