Preheat oven to 450°. In a food processor, whirl garlic cloves, zest, 1/3 cup marjoram leaves, and 1 tsp. each salt and pepper until minced. Blend in oil.
Remove any ties from lamb and open it up in a rimmed baking pan. Trim fat (leave a thin layer on the outside). Smear meat all over with marjoram mixture. Using kitchen twine, tie lamb crosswise at about 1 1/2-in. intervals and lengthwise once or twice to form a neat roast. Set in pan fat side up.
Roast lamb until browned, 20 to 25 minutes. Meanwhile, cut garlic head in half crosswise, set cut sides down on an oiled piece of foil, and seal foil into a package.
Reduce heat to 300°; set garlic next to meat in pan and bake until very soft when squeezed, 50 to 60 minutes; stir 1/2 to 1 cup broth into drippings if needed to prevent scorching. Let garlic cool. Cook meat until an instant-read thermometer inserted in thickest part reaches 130° for medium-rare.
Transfer lamb to a cutting board (save pan drippings for sauce); tent with foil.
Squeeze garlic from peels into a blender. Stir cornstarch with 1 1/2 cups broth until smooth; whisk into drippings, then purée in blender. Heat sauce in a saucepan, stirring, until boiling. Mince remaining marjoram and stir into sauce. Pour into a gravy boat.
Snip twine from lamb, then cut thickly crosswise. Spoon some sauce on top and garnish with marjoram sprigs. Serve remaining sauce on the side.
*Order ahead of time from your butcher.
Note: Nutritional analysis is per serving.