Preheat oven to 450°F.
Break cauliflower into small florets and slice each in half so they have a flat side.
Toss with olive oil, kosher salt, and black pepper.
Spread cut-side down on a sheet pan in a single layer.
Roast until deeply caramelized and golden on the flat side, about 20-25 minutes.
Combine avocado, basil, chives, parsley, garlic, olive oil, and salt in a blender or food processor.
Blend until smooth and vibrant green, adding water 1 tablespoon at a time to reach a drizzleable consistency.
Taste and adjust salt as needed.
Heat the avocado oil in a small pan over medium until it reaches 325-375°F. Carefully add the dried capers and stand back to avoid oil splatters. Fry the capers for a few minutes, gently shaking the pan, until they turn crispy and golden brown. Test a couple. Lift them out with a slotted spoon onto a paper-towel-lined plate, and strain the oil into a jar to save for dressings.
Place roasted cauliflower florets on each cracker, caramelized side up.
Drizzle avocado green goddess over the cauliflower.
Finish with shaved parmesan, crispy capers, and flaky sea salt.