Preheat oven to 350°F. Cover springform pan with some oil, then line bottom with a round of parchment paper. Oil parchment.
Beat together yolks and 1/2 cup sugar in a large bowl with an electric mixer at high speed until thick and pale, about 3 minutes. Reduce speed to medium and add olive oil (3/4 cup) and reserved lime juice, beating until just combined (mixture may appear separated).
Transfer batter to springform pan and gently tap against work surface once or twice to release any air bubbles. Sprinkle top evenly with remaining 1 1/2 tablespoons sugar. Bake until puffed and golden and a wooden pick or skewer inserted in center of cake comes out clean, about 45 minutes.
In the last 20 minutes, remove cake from oven and add the grapefruit slices, place back in the oven to continue cooking. Cool cake in pan on a rack 10 minutes, then run a thin knife around edge of pan and remove side of pan.
Cool cake to room temperature, about 1 1/4 hours. Remove bottom of pan and peel off parchment, then transfer cake to a serving plate. Dust lightly with powdered sugar, cut and serve with dressing.
This cake was adapted from Gourmet, 4-2006.