To make the simple syrup: combine all ingredients in a saucepan over medium heat. Bring to a boil and then reduce to a simmer. Allow to simmer 10-15 minutes, stirring occasionally, with the lid on (but vented). Strain into a jar, label, and store in the fridge. This should last at least a few weeks.
To make the slushie: combine all ingredients in a blender or food processor and pulse until the ice is broken down and it starts to take on a slushie consistency. Taste and adjust lemon juice/fennel simple syrup as needed. Pour into cups and enjoy!