Preheat oven to 350 degrees; grease cupcake tins.
Mix together sugar and butter. Add eggs that have been well-beaten, lemon juice and zest; mix well. Add salt, flour and baking powder and mix well again. Add milk; fold in cooked bulgur. Pour batter into greased cupcake tins or paper cupcake holders. Bake for 19-21 minutes.
To cook bulgur: Using 1/2 cup dry bulgur, bring to a boil in 1-1/4 cups water. Let boil for 5 minutes. Turn down heat to simmer for 12 more minutes; drain and cool.
Cupcake glaze: 3/4 cup powdered sugar with 2 Tbsp. lemon juice