Prepare & cook the lamb
In a large non-reactive dish, mix 2 Tbs. oil with the wine, mustard, garlic, tarragon, 2 Tbs. salt, and 1 tsp. black pepper. Add the lamb and coat with the marinade, cover, and refrigerate, flipping occasionally, for at least 8 hours and up to a day.
Position a rack in the center of the oven and heat the oven to 450°F. Put the lamb on a large cutting board and cut away any fatty patches. Set the lamb in a large roasting pan. Brush with the remaining Tbs. oil and sprinkle with pepper.
Roast the lamb until it starts to brown on top, 12 to 15 minutes. Reduce the oven’s heat to 325°F and roast until an instant-read thermometer inserted into a thicker part of the lamb registers 135°F for medium-rare, 30 to 35 minutes. Transfer the lamb to a cutting board, tent with foil, and let rest for 10 minutes.
Make the sauce
In a medium saucepan over medium heat, heat the oil with the garlic, stirring, until the garlic sizzles steadily and just starts to turn golden at the edges, about 2 minutes. Remove from the heat and add 3/4 cup water and the vinegar. Whisk in the sugar until dissolved. Stir in 1/2 tsp. pepper. Taste and season the sauce with more sugar, salt, and pepper if needed. Let sit at room temperature while the lamb roasts.