In a medium bowl, make compound herb butter by combining softened butter, thyme, sage, parsley, chives, and rosemary (this can also be done in a food processor). Turn out onto parchment or plastic wrap, and roll into a log, 1 1/2 to 2 inches in diameter. Chill until firm, or freeze for up to 1 month.
Heat grill or grill pan. Form 4 (8-ounce), 1-inch-thick burgers. Cut 4 (1/8-inch-thick) slices of compound butter from the log. Make an indentation in the center of each burger, and place half of a compound-butter slice inside. Reshape meat to cover butter, making sure it is not visible from either side; season both sides with salt and pepper.
Oil grill with a small amount of vegetable oil to prevent sticking. Grill burgers for 5 to 7 minutes per side for medium doneness. Remove from grill, and place each burger on a roll. Serve garnished with lettuce and tomato.
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