In a large saucepan, bring the water and the 1 teaspoon salt to a boil. Add the bulgur, cover the pan. Remove the pan from the heat and let the bulgur sit for 10 minutes.
Lay the eggplant slices on one or two lightly greased baking trays. Bake them in the oven for 15 minutes or until the eggplant has softened but is not browned. Remove the eggplant from the oven and lower the temp to 180 degrees C.
While the eggplant is baking, make the bechamel sauce: Melt the butter in a saucepan over medium heat. Add the garlic and cook it, stirring often, for 1 minute. Add the flour and stir constantly for 1 minute. Slowly add the milk, 1/2 cup at a time, whisking well after each addition. Simmer the mixture, stirring frequently, for 5 minutes. Remove the pan from the heat.
Sprinkle the basil, nutmeg, salt and pepper into the saucepan of bechamel sauce.
Spoon the bulgur into a 20x30cm casserole dish and pat down well. Lay the eggplant slices on the bulgur, overlapping them in rows.
Squeeze the tomatoes through your hands to break them up, and spread the broken tomatoes and their juice over the eggplant.
When the bechamel sauce has cooled a bit whisk the egg into it. Pour the sauce over the tomatoes.
Bake the moussaka, uncovered, for 45 minutes. Slice it as you would lasagne, and serve.