Butter and flour a tube cake pan. Set aside.
In a large bowl or the bowl of a stand mixer, cream butter and cream cheese together until completely combined. Add both sugars, vanilla, and eggs; mix well, scraping down the sides of the bowl as necessary.
Add flour, cinnamon, and salt, mix until all dry ingredients are combined.
Return to your bowl of bourbon-soaked peaches. Drain liquid into a measuring cup and set aside (we’ll use this later to make a bourbon soak that goes on the cake after it bakes!)
Add ¼ cup flour and ½ tsp ground cinnamon to the peaches; toss until peaches are evenly coated. Fold peaches into the cake batter.
Pour batter into the prepared cake pan. Place in a cold oven and bake on 325°F for 1 hour and 15 minutes to 1 hour and 30 minutes. To check for doneness, insert a toothpick into the center of the cake. If it comes out clean, the cake is done! A couple of crumbs clinging to the toothpick are okay, you just don’t want liquid cake batter. If that happens, back into the oven it goes, checking in 5 to 10 minute increments.