To make the gazpacho, cut a 2-inch piece off the end of the cucumber and set it aside for garnish. Roughly chop the remaining cucumber and transfer it to a high-speed blender.
Add the avocado, scallion, garlic, olive oil, water, kosher salt, and vinegar and blend until smooth. Chill in the fridge for at least 1 hour.
For the garnish, finely dice the reserved piece of cucumber and toss in a small bowl with the mint leaves, apple cider vinegar, a pinch of flaky salt,and minced shallot.
Remove the gazpacho from the fridge, taste, and season with kosher salt.Divide between two bowls and spoon over the chopped cucumber relish. Drizzle each bowl with olive oil and finish with cracked pepper.