Preheat the grill 30 minutes in advance, burning the wood down until you have a red-hot coal base.

To make the patties:

Divide the meat into four portions and shape them into patties. Season both sides of the patties heavily with salt and pepper, and place them on the grill. Then leave them alone–you want to let the outside caramelize, and moving the burgers too early can rupture their surface and allow the juice to leak out. Once the burgers move easily when gently prodded, flip them over. Cook to your desired doneness--rare is great!

To serve, encourage your guests to build their own burgers on a bun with the sliced white cheddar and their choice of marinated onions, mayonnaise, tomato slices, lettuce, ketchup, and/or mustard. Don’t forget the pickles and the fries!

To make the House-Made Buns:

Put the milk in a small saucepan and warm it over very low heat until lukewarm.

Remove the pan from the heat. Sprinkle the yeast over the milk, stir, and set it aside for 5 minutes to activate.

Butter a large bowl and set it aside.

In an electric mixer fitted with the dough hook attachment, combine the yeast mixture with half the flour on low speed. Then, over a 1-minute period, add the remaining flour along with the sugar, salt, egg, and butter. Increase the speed to medium and mix for 2 minutes. Then turn the speed to high and mix for 2 minutes more. Transfer the dough to the prepared bowl, cover it loosely with plastic wrap, and set it aside in a warm area for 45 minutes to 1 hour, until the dough has doubled in size.

Turn the dough out onto a floured surface. Divide it into 6 or 7 equal pieces, and arrange them in a row on the surface. Keeping the other portions covered with a kitchen towel so they won’t dry out, roll each piece into a ball. Leave them, covered, on the surface for another 10 minutes to relax the gluten. Then, using a rolling pin, flatten the balls into rounds that are 3½ to 4 inches in diameter. Place the buns on a baking sheet lined with parchment paper, put the baking sheet inside a large plastic bag, and tie the open end closed. Place the pan in a warm area of the kitchen and let the buns rise until they have doubled in size, 30 to 45 minutes.

Meanwhile, preheat the oven to 375°F.

Remove the sheet pan from the bag, brush each bun with water, and then sprinkle the sesame seeds on top. Bake the buns for 20 to 25 minutes, until golden brown.

Let them cool for at least 10 minutes before serving. Slice in half and serve.

To make the Marinated Onions:

Soak the onion slices in a bowl of ice water for 15 minutes. Drain the onions, place them in a nonreactive bowl, and drizzle the lemon juice and champagne vinegar over them. Toss in the parsley, chives, and scallions. Drizzle with the olive oil, and season with the salt and pepper. Marinate at room temperature for at least 30 minutes. The marinated onions can be made up to 8 hours in advance.