Cream together the softened butter and 2 cups of granulated sugar in a mixer on medium speed for about five minutes. Beat in each egg one at a time until fully combined. Add the zest from all four oranges.
In a large bowl, mix together the flour, baking powder, baking soda, and kosher salt. In another bowl, combine 1/4 cup of orange juice with the yogurt and vanilla extract.
Gradually add the flour mixture and yogurt mixture alternately into the butter mixture in three additions until everything is combined smoothly.
Pour the batter evenly into two greased loaf pans. Bake in a preheated oven at 350 degrees Fahrenheit for about 45–55 minutes or until golden brown and a toothpick inserted into the center comes out clean.
Prepare by cooking together the remaining 1/2 cup sugar with 1/2 cup orange juice over low heat until sugar dissolves completely. Spoon the syrup over each loaf while they’re still warm.
Mix together the powdered sugar with 3 tablespoons of orange juice until smooth. Pour this glaze over each cooled loaf allowing it to set before serving.