Preheat the oven to 375 degrees F (190 degrees C). Line 2 baking sheets with parchment paper.
Beat eggs in a large bowl using an electric mixer until fluffy. Add oil, orange zest, and juice; mix well. Beat in sugar slowly.
Combine flour, baking powder, and vanilla powder in a separate bowl. Slowly add to the egg mixture, 1 cup at a time, mixing well after each addition. Beat until almost blended; mix the rest by hand.
Roll dough into 2 ropes; cut into 3- to 4-inch pieces. Twist 2 pieces together or roll individual ropes into circles to make round cookies.
Place cookies 2 inches apart on the prepared baking sheets.
Bake in the preheated oven until edges are golden but cookies are not yet brown, about 10 minutes. Let cookies cool completely, at least 30 minutes.
Meanwhile, slowly mix lemon juice into a bowl of confectioners' sugar to make a runny icing. Line a few trays with waxed paper. Dip cooled cookies into the icing and transfer them onto the trays to harden.
