Slash the skin and fat all over the duck in a one inch diamond pattern, being careful not to cut into the flesh. Season the duck with the salt, inside and out, and rub the salt into the slashes in the skin. Put the duck on a rack over a roasting pan or baking sheet. Store in the refrigerator, uncovered, at least overnight, or up to 48 hours before cooking. This lets the skin dry, and gives the salt time to dry brine the duck.

Remove the duck from the refrigerator 2 hours before cooking to let it come to room temperature. Juice the lime and reserve the lime juice for the glaze, then put the lime halves and a handful of thyme and rosemary inside the duck cavity. Fold the wingtips back underneath the wings, then truss the duck. Skewer the duck on the rotisserie spit, securing it with the spit forks.

Set the grill up for rotisserie cooking at medium-high heat (400°F). For my Weber Summit, I remove the grill grates, turn the two outer burners (burners 1 and 6) to high, and turn the infrared burner to high. Then I put my drip pan in the middle, over the unlit burners, and let the grill preheat for ten to fifteen minutes. After preheating, I turn the lit burners down to medium-high.

While the grill is pre-heating, halve the new potatoes, toss with 2 teaspoons kosher salt, put them in a microwave safe bowl, and seal the top of the bowl with plastic wrap. Microwave for 5 minutes to par-cook, and reserve for later

Put the reserved lime juice, honey, minced thyme, and rosemary in a microwave safe bowl and microwave for 1 minute. Stir until the honey and lime juice are evenly mixed.

Put the spit on the grill, and cook the duck with the lid closed. After 45 minutes, pour the potatoes into the drip pan underneath the duck, and turn off the infrared rotisserie burner if the duck is browning well. The duck is fully cooked when the temperature in the thickest part of the thigh is 180°F; total cooking time is about an hour and a half. Once the duck is cooked through, brush it with an even layer of the glaze using the herb brush. Close the lid and cook for five more minutes to thicken the glaze, then brush the duck with another layer of glaze and remove from the grill.

Remove the duck from the spit, and transfer to a platter. Be careful - the spit is blazing hot. Remove the twine from the duck, then brush the duck once more with the glaze. Remove the potatoes from the drip pan with a slotted spoon, then taste and sprinkle with a little more salt if necessary. Let the duck rest for 10 minutes before carving.