Trim the root of the leek, leaving ends intact to hold the leaves together, then halve lengthwise. Rinse well under running water to flush out any grit trapped between the leaves. Cut each half into 3-inch lengths, keeping leaves together. Put leeks in a large frying pan with water to cover and 1 teaspoon salt. Simmer over medium heat until the leeks are tender, about 6 minutes. Drain the excess water, add 2 tablespoons butter, and cook over medium heat until the leek edges are golden brown and sweet.
Cook the bacon in a medium frying pan, until just crisp. Transfer to paper towels to drain.
Preheat oven to 350 degrees F. Brush a 9-inch glass or ceramic pie pan with 2 tablespoons butter and sprinkle the grated Parmesan evenly on top. Put pan on a baking sheet.
Whisk the single cream, eggs and yolks in large glass measuring cup. Season with 1/2 teaspoon salt, pepper, and nutmeg. Spread half the Gruyere evenly in the pan, crumble the bacon on top; repeat with remaining cheese. Place the leeks, browned side up, on the cheese and pour the custard over the fillings.
Bake until the quiche is just set in the center, about 40 to 50 minutes. Cool completely on a rack before serving.