Special equipment: a 9-inch springform pan (or a 9-inch glass baking dish)
Position an oven rack in the center of the oven and preheat to 350 degrees F. Thoroughly grease the bottom and sides of a 9-inch springform pan with butter.
Make the batter: In the bowl of an electric mixer fitted with the whisk attachment, beat together the butter and sugar on high speed until they lighten in color, 5 to 8 minutes. Slowly beat in the eggs one by one, then pour in the olive oil and milk and mix to combine.
Mix the dry ingredients: In a medium bowl, sift together the flour, baking powder and salt. Grate 5 or 6 light "grates" of the lemon zest over the flour mixture.
Finish the batter: Remove the bowl from the mixer and use a rubber spatula to fold the flour mixture into the egg mixture. Fold in about 1 cup of the grapes. Stir only enough to blend and gently so as not to bruise or break too many grapes.
Bake the cake: Pour the batter into the prepared pan and place it in the center of the oven. Bake until a toothpick inserted in the center comes out clean, 40 to 45 minutes. Let cool for about 10 minutes in the pan.
Make the glaze and serve the cake: Meanwhile, combine the honey and ginger in a small saute pan. Bring to a light simmer over low heat. When it bubbles, thickens and turns light brown, 2 to 3 minutes, add the remaining 1/2 cup grapes and the juice from 1/2 of the lemon. Remove from the heat and allow to cool.
Serve slices of the cake with some of the grape-ginger mix spooned over it. Serve with tangy Greek yogurt or a scoop of lemon sorbet on the side.