For the best results, use farm-stand corn and make the pudding the same day you buy the corn.
Step 1: Set up the grill for direct grilling and preheat to high.
Step 2: Lightly brush each ear of corn with olive oil and season with salt and pepper.
Step 3: When ready to cook, place the corn on the hot grate and grill until golden brown on all sides, 2 to 3 minutes per side(8 to 12 minutes in all), turning with tongs. Transfer the grilled corn to a cutting board and let cool.
Step 4: Cut the corn kernels off the cobs, using lengthwise strokes of a chef’s knife. Break 3 of the cobs in half and place them in a saucepan with the cream over medium heat and bring to a simmer. Let the cream simmer gently for 15 minutes to infuse it with corn flavor. Remove the pan from the heat and let the cream cool.
Step 5: Place half of the corn kernels in a food processor and puree to a smooth paste. Add the egg yolks and process to mix. Strain in the cooled cream and pulse just to mix. Transfer the corn mixture to a large bowl and stir in the remaining whole corn kernels and the nutmeg. Season with salt and pepper to taste. Taste for seasoning, adding sugar and/or more nutmeg as necessary; the corn mixture should be highly seasoned.
Step 6: Set up the grill for indirect grilling and preheat to medium. If using a gas grill, place all of the wood chips or chunks, if desired, in the smoker box or in a smoker pouch and run the grill on high until you see smoke, then reduce the heat to medium. If using a charcoal grill, preheat it to medium, then toss all of the wood chips or chunks, if desired, on the coals.
Step 7: Using a stand mixer or a clean metal bowl and a hand mixer, beat the egg whites with the cream of tartar until soft peaks form (they should be firm and glossy but not dry). Gently fold the egg whites into the pureed corn mixture with a rubber spatula. Lightly oil the baking dish, then spoon the corn mixture into it. Don’t over fold, or you’ll deflate the egg whites.
Step 8: Place the filled baking dish in the center of the hot grate, away from the heat, and cover the grill. Grill the pudding until puffed, browned on top, and cooked through, 20 to 30 minutes To test for doneness, insert a toothpick or metal skewer in the center of the pudding; it should come out clean. Serve the pudding at once.