Preheat oven to 350°F. Line a standard (12-cup) cupcake pan with paper liners; set aside.
In the bowl of an electric mixer, on medium speed, beat together oil and sugar until smooth and creamy.
Add vanilla, salt, baking soda, baking powder, and eggs. Beat until combined.
Alternately add half the flour and half the pomegranate juice, beating after each addition until incorporated.
Spoon batter into prepared pan, filling each cup about three-quarters full.
Bake for 16-18 minutes, until the tops are set. Remove from oven; cool completely before glazing.
Prepare the glaze: In a small bowl, combine powdered sugar with 2 tablespoons pomegranate juice; mix until smooth. Gradually add an additional 1-3 teaspoons juice if needed to form a thick but spreadable glaze.
Dip the tops of the cooled cupcakes into the glaze, allowing excess to drip back into the bowl. Garnish with pomegranate seeds, if desired.
Recipe from Something Sweet, by Miriam Pascal, reproduced with permission from the copyright holders, ArtScroll/Mesorah Publications.