Place a rack in the middle of the oven and heat oven to 325ºF. Lightly butter a bundt pan and dust with flour, tapping out the excess.
Chop one apple into 1/4-inch dice, leaving the peel on. Grate the other apple on the large holes of a box grater. Set both aside.
Whisk the flour, baking soda, salt, and spices, together in a large bowl.
Combine butter, granulated sugar and brown sugar in the bowl of a stand mixer and using the paddle attachment, beat on medium until the mixture is pale and fluffy, about 3 minutes.
Whisk together the eggs and vanilla and slowly add, with the mixer on low speed, to the butter and sugar. Add the flourSift onto a paper plate, fold it like a taco, and feed it into the mixer. one-third at a time and beat on low just until combined after each addition. Stir in the apples, pecans, and ginger.
Transfer the batter to the prepared bundt pan, the batter is thick and will fill the pan. Bake for 75 minutes, rotating the pan after 30 minutes. The cake is done when it pulls away from the sides of the pan, springs back when pressed and the internal temperature reaches 205°F.
Cool the cake in the pan on a rack for 30 minutes. Invert and remove the cake from the pan. Cool completely on the rack before glazing.
Combine the powdered sugar, rum, and water in a small mixing bowl and whisk until smooth. Pour the glaze onto the bundt cake and sprinkle with turbinado sugar. Let the glaze set for at least 30 minutes before serving.