Place the frozen peaches, cinnamon, ginger, honey, ice cubes, and water or juice in a blender.
Pulse the blender on low speed to start breaking up the fruit and ice, then increase to high and blend until the mixture is smooth and icy, about 30-45 seconds. Listen for a creamy whirl and watch as the mixture turns a vibrant, slushy consistency.
Pause and scrape down the sides if necessary, then resume blending until uniform and frosty in texture.
Taste the slushie and, if desired, add a splash more honey or syrup for extra sweetness, then blend briefly to incorporate.
Pour the icy peach mixture into glasses, ensuring each is filled generously with the fragrant, smooth slush.
Serve immediately with a straw or spoon, enjoying the refreshing, lightly spicy flavor and the cool, textured feel of the frozen peaches and ice.