6 tablespoons (¾ stick margarine), room temperature
1 tablespoon finely chopped fresh tarragon
1 tablespoon finely chopped fresh basil
1 tablespoon finely chopped fresh Italian parsley
1 teaspoon finely grated lemon peel
1 teaspoon fresh lemon juice
1½ pounds ground beef (15% fat)
Vegetable oil (for brushing)
4 sesame seed hamburger buns
1 large tomato, thinly sliced crosswise
1 bunch arugula
Mix margarine, all herbs, lemon peel, and lemon juice in small bowl. Season with salt and pepper. Measure 1/3 cup herb margarine; transfer to sheet of plastic wrap (reserve remaining margarine in bowl for spreading on buns). Using plastic wrap as aid, form margarine into 3-inch long log; wrap plastic around to seal. Freeze until firm, about 30 minutes. Cut crosswise into 4 rounds. Flatten rounds into 2-inch diameter disks.
Divide meat into 4 equal pieces. Using damp hands, form each piece into a bowl. Using thumb, make deep wide indentation in center of each ball. Press 1 lemon-margarine round flatly into indentation, then press meat securely over butter to enclose.
Flatten each burger into 3½-inch diameter patty, leaving margarine rounds horizontally in center of each burger.
Do ahead: Herb margarine and burgers can be made 6 hours ahead. Place burgers on baking sheet, cover with plastic wrap, and chill. Cover and chill herb butter in bowl; bring to room temperature before continuing.
Brush barbecue rack with oil. Prepare barbecue (high heat). Sprinkle both sides of burgers with salt and pepper. Spread remaining margarine over cut sides of buns. Grill burgers until cooked through, 4 to 6 minutes per side. Grill buns until slightly charred, about 1 minute per side.
Place burgers on bun bottoms. Top with tomato slices and arugula leaves. Cover with bun tops and serve.