Add peaches, water, and salt to a large skillet over medium heat. Let cook until bubbling, then mash with a fork slightly, to smooth. Add ginger, optional bourbon, lemon juice, vanilla extract, and brown sugar. Stir to prevent sticking, if things are cooking too quickly, turn down the heat and add a bit more water. Cook for a couple of minutes more, until you have the texture of a thick but soft sauce. Remove from heat and set aside.

Next, in another small pan, add olive oil, oats, cinnamon, brown sugar, and nuts if using. Let entire mixture toast in the pan until fragrant and golden, about 5 minutes.

To assemble floats, later ice cream, peach sauce, and oat crumble in 2 or 3 tall glasses. One filled ¾ of the way, top with ginger beer. Enjoy immediately.