Preheat your oven to 350°F (175°C) and grease a 2-quart baking dish.
In a large mixing bowl, combine sliced peaches with sugar, cinnamon, salt, and bourbon. Toss gently until the peaches are evenly coated, then spread them out in the prepared baking dish.
To make the crumble topping, mix flour, brown sugar, oats, and toasted almond slivers in a separate bowl.
Add the cold butter cubes to the dry mixture. Using your fingers or a pastry cutter, work the butter into the mixture until it resembles coarse crumbs with some pea-sized pieces.
Sprinkle the crumble evenly over the peaches, covering all the fruit surface.
Place the baking dish in the oven and bake for about 40 minutes, or until the topping is golden brown and bubbling at the edges.
Remove the peach crisp from the oven and let it rest for a few minutes. The fruit will thicken slightly, and the topping will crisp up further as it cools.
Serve warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.