Preheat oven to 350F, thoroughly grease a 10-15" bundt pan (or 9x9 square pan) with butter and lightly dust with flour. Set aside.
In a large bowl combine flour, cardamom, baking powder, baking soda, salt, grapefruit zest. Whisk until combined and set aside.
In a medium bowl whisk together eggs, Greek yogurt, and granulated sugar. Gently pour in 1/2 cup of grapefruit juice, milk, and cooled butter or oil. Gently stir together.
Carefully pour wet ingredients into large bowl of dry ingredients. Use large rubber spatula to gently combine, avoid over-mixing the batter.
Transfer cake batter into greased bundt pan. Make sure oven rack is in middle of oven. Bake for 25-35 minutes, or until inserted toothpick comes out with little crumbs.
Allow cake to cool in pan for 20 minutes before removing. Make the glaze while cake is cooling: Combine powdered sugar and grapefruit juice in a small bowl.
Once cake has cooled, gently bang pan on counter to loosen cake. Flip onto cooling rack. Place plate or baking sheet under cooling rack to catch glaze. In a zigzag pattern pour glaze over cake.
Once glaze has set, you can slice, serve, and enjoy!