Moussaka

To prepare meat sauce: Heat 2 tablespoons oil in a large pot over medium-high heat. Add onions and garlic; cook, stirring occasionally, until soft, about 3 minutes. Add beef and cook, stirring occasionally and breaking up any large pieces with the back of a wooden spoon, until no longer pink, about 6 minutes. Add tomatoes and their juice, water, cinnamon stick and 1/4 teaspoon each salt and pepper; bring to a simmer. Reduce heat to maintain a simmer and cook, stirring occasionally and breaking up the tomatoes with the back of the wooden spoon, until thick and the liquid is mostly evaporated, about 35 minutes. Remove from heat; discard the cinnamon stick.

Meanwhile, prepare béchamel: Melt butter in a large saucepan over medium heat. Add flour and cook, whisking, until just starting to brown, about 1 minute. While whisking, slowly add milk. Continue cooking, whisking frequently, until the sauce has thickened, about 8 minutes. Remove from the heat and immediately whisk in 1 cup graviera (or Pecorino) cheese, egg, 1/8 teaspoon each salt and pepper, and nutmeg.

To prepare moussaka: Position racks in upper third and center of oven; preheat broiler to high. Line two baking sheets with foil. Brush both sides of eggplant slices with oil and sprinkle with salt and pepper. Arrange in an even layer on the prepared pans. Broil the eggplant, flipping once and swapping the pans between racks, until soft and starting to brown, about 20 minutes. (Alternatively, preheat grill to medium. Grill the eggplant, flipping once, until browned and softened, about 4 minutes per side.)

Preheat oven to 375°F. Layer half of the eggplant in a 9-by-13-inch baking dish. Cover with the meat sauce. Sprinkle with feta (or graviera) cheese and top with the remaining eggplant. Pour the béchamel over the eggplant and smooth with a spatula. Sprinkle with breadcrumbs. Bake the moussaka until bubbling at the edges, about 45 minutes. Let stand for 10 minutes before serving.