Add the chopped peach, thyme, maple syrup, and lemon juice to a cocktail shaker.
Gently muddle just until the peach releases its juices and the thyme becomes fragrant.
Don’t pulverize the peach. Give it just a few firm presses with your muddler to release the juice while leaving the fruit mostly intact. The more you mash it into a purée, the faster it will clog your fine-mesh strainer.
Add the bourbon and almond liqueur, then fill the shaker with ice.
Shake vigorously until well chilled.
Double strain into two rocks glasses over large ice cubes.
For easier straining, use a quick homemade peach purée instead of muddling the peaches
Garnish each with a fresh peach slice and sprig of thyme.