Preheat oven to 350°F. Grease a 10-inch Bundt pan and dust with flour to cover all the sides.
Whisk flour, baking powder, salt, cinnamon, allspice and nutmeg in a medium bowl.
In a large bowl, add butter and beat until creamy. Add the sugar to the butter and continue to beat until light and fluffy. One at a time, beat in the eggs until well combined. Add in yogurt and vanilla and beat until all the ingredients are incorporated and the mixture is smooth.
Fold in half of the flour and mix until combined, then fold in the other half of the flour. Mix until batter has no lumps. Gently fold in the cubes of cream cheese into the batter.
Make caramelized peaches:
Melt 4 tablespoons of butter in a large skillet over medium heat. Whisk in the brown sugar until it dissolves and mixture starts to bubble.
Add peaches to the pan and gently stir for 4 minutes, fully coating peaches in caramel. Pour the peach mixture into the bottom of the greased Bundt pan.
Spread the cake batter over the peaches. Bake for 1 hour, or until a toothpick is inserted and comes out clean. Cool the cake in Bundt pan for a minimum of 20 minutes, then invert onto a plate.
In a medium bowl, beat the cream cheese and butter until smooth. Sift in the powdered sugar and beat until combined. Add the cinnamon and vanilla and mix together.
Drizzle icing over the top of the cooled cake and serve.