Heat oven to 325 degrees and position a rack in the middle of the oven. Butter and flour a 9-inch cake pan, preferably a springform pan.
With an electric mixer, cream the butter and sugar, then add honey and whip for 1 minute, until fluffy. Beat in eggs one at a time, until well incorporated, then whip for 2 minutes. Stir in grated ginger, candied ginger, and lemon zest.
Whisk together flour, cinnamon, salt and baking powder and add to bowl, mixing briefly to make a stiff batter. Pour batter into prepared pan.
With a paring knife, cut slits in each of the apple quarters on the rounded, outer part of the wedge, slicing partway through at 1/8-inch intervals. Arrange apple quarters slit-side-up over the batter. Sprinkle surface with 1 tablespoon sugar.
Place cake pan on a baking sheet and put on middle rack of oven. Bake for about 45 minutes, or until an inserted skewer emerges dry. (It took about 52 minutes for me) If cake is browning too rapidly, tent with foil until done. Cool on a rack, then carefully unmold.
Make the Glaze
Put sugar, honey and lemon juice in a small saucepan over medium heat, stirring until sugar is dissolved and mixture bubbles, about 2 minutes. Paint surface of cake and apples with warm glaze. Cake will keep for several days, tightly wrapped, at room temperature.