Combine apricots, sugar, orange zest, orange juice and water in a medium saucepan. Bring to a boil; reduce heat to a simmer and cook, stirring occasionally, until the apricots are very tender, about 10 minutes. Stir in bulgur and increase heat to high. Return to a boil; reduce heat to a low simmer and cook, stirring occasionally, until the bulgur is tender, about 20 minutes. (The mixture will be the consistency of cooked oatmeal.) Remove from the heat and let cool, uncovered, for 10 minutes.

Position a rack in the center of the oven; preheat to 350 degrees F.

Whisk egg yolks and milk in a large bowl until well combined. Slowly whisk in the bulgur mixture.

Beat egg whites in a medium bowl with a mixer on medium-high speed until stiff peaks form. Fold into the bulgur mixture using a rubber spatula.

Transfer the batter to an 8-inch-square baking dish. Push brown sugar through a sieve evenly over the batter. Place the baking dish in a roasting pan and transfer to the oven. Pour very hot tap water into the roasting pan until it comes about halfway up the sides of the baking dish. Bake until the cake is puffed and golden, 30 to 40 minutes.

Carefully remove the baking dish from the hot water, transfer to a wire rack and let cool to room temperature before serving. Top each serving with some Custard Sauce and a sprinkling of pistachios.

Note: A staple grain of Lebanese cooking, bulgur is made by parboiling, drying and coarsely grinding or cracking wheat berries. Don't confuse bulgur with cracked wheat, which is simply that--cracked wheat. Since the parboiling step is skipped, cracked wheat must be cooked for up to an hour whereas bulgur simply needs a quick soak in hot water for most uses. Look for it in the natural-foods section of large supermarkets, near other grains, or online at kalustyans.com, lebaneseproducts.com.

MAKE AHEAD TIP: Cover and refrigerate for up to 3 days. Serve chilled or at room temperature.