Heat oven broiler. Arrange grapefruit slices in an even layer on an aluminum foil–lined baking sheet fitted with a wire rack; sprinkle with 3 tbsp. sugar. Broil, rotating pan as needed, until slightly caramelized, about 7 minutes; set aside.
Heat oven to 325°. Whisk flour, salt, and baking soda in a bowl; set aside. In another bowl, and using an electric hand mixer, cream remaining sugar and the butter until fluffy. Add eggs one at a time, beating well after each addition. Add zest, buttermilk, and vanilla; mix until combined. With the motor running, slowly add dry ingredients until smooth. Spread batter evenly into a 9" × 13" baking dish; bake until a toothpick inserted in the middle of the cake comes out clean, 45 minutes to 1 hour. Let cake cool, then arrange reserved grapefruit slices, overlapping slightly, on top.
Whisk juice and confectioners' sugar in a bowl until smooth; drizzle evenly over cake. Let cake sit 30 minutes to set glaze before serving.