Prepare Dry Ingredients: Sift the flour, salt, baking powder, and baking soda into a medium mixing bowl. Whisk well and set aside.
Mix Wet Ingredients: In a large mixing bowl, combine the sugar, oil, and vanilla. Zest 2 oranges directly into the bowl. Squeeze both oranges, strain the juice, and add 1/2 cup of this juice to the wet ingredients. Mix with a wire whisk until well incorporated, about 2 minutes.
Combine Ingredients and Knead: Add the flour mixture to the wet ingredients and combine with a rubber spatula until just combined. Knead the dough by hand until smooth, about 2 minutes. Let rest for 5 minutes.
Shape Cookies: Using an ice cream scoop (1 1/2 Tbsp), scoop the dough into even balls (25 g) and place onto a sheet pan lined with parchment paper. Alternatively, divide the dough into equal balls by hand. This recipe yields 40 pieces.
Preheat Oven: Preheat oven to 350 degrees F (180 degrees C) with the oven rack in the center.
Form Cookies: Shape the dough into a small ball, then into a log (11 cm). Join the ends of the log to form a ring.
Bake: Place cookies 1 inch apart on ungreased baking pans. Use 2 half sheet pans and 1 quarter sheet pan. Bake 1 sheet at a time on the center rack for 12 minutes or until golden on both sides. Let cool for 5 minutes on the baking sheet, then transfer to a cooling rack to cool completely.
Storage: Store in an airtight container at room temperature.