Melt the butter in a small saucepan. Stir in the chicken broth, juice, soy sauce, onion, brown sugar, ginger and cardamom. Season with salt and pepper. Cook over medium heat until it comes to a gentle boil. Let it cook for about 5 minutes.
In a small bowl, whisk together the cornstarch and the water. Add the cornstarch mixture to the sauce and cook just until the sauce starts to thicken up. (This will probably happen very quickly.) Remove the sauce from the heat.
Meanwhile, pour a layer of vegetable oil into a large saute pan and warm over medium heat. Add the flour to a shallow dish and season with salt and pepper. Add the egg to another shallow pan and add about a teaspoon of water. Lightly whisk.
Working in 3-4 batches, take some of the chicken and dip it in the egg mixture. Allow some of the egg to drip off, and put the chicken in the flour mixture to coat. Use tongs to transfer the chicken to the hot oil and pan fry, turning as necessary, until the chicken is golden brown and cooked through. Remove to a paper towel lined plate. Repeat with the remaining chicken, adding more oil as necessary.
Put all of the cooked chicken into a large bowl. Pour the sauce over the top and stir to coat the chicken. Serve over rice and top with sliced green onions.
