Make the sauce - Mix the blackberries, habaneros, garlic, honey, vinegar, and salt in a sauce pot and bring to a simmer. Reduce to low and cook for about a half hour. Allow to cool slightly and blend for about 30 seconds with a hand blender until mostly smooth. Strain through a mesh strainer into a container to store until ready to use. If making ahead of time, store in the fridge for up to a week.
Make the quick pickled onions - Put the onions into a container, in a microwave safe measuring cup, mix together the vinegar, sugar, and salt and microwave for about 1 minute until hot. Pour this mixture over the onions, top with a little water, cover, and set aside until ready to use. If making ahead of time, store in the fridge for up to 4 days.
Marinate the chicken- Mix the buttermilk, garlic, and salt in a zip top bag and add the chicken. Set aside in the fridge for an hour.
Cook the chicken - Preheat the oil to 350 or air fryer to high/400. Mix the flour, cornstarch, salt, pepper, paprika, and garlic powder together in one shallow bowl. In another, beat the egg. One by one, remove a chicken piece from the marinade, draining off excess liquid, and dip it into the flour mix. Then shake off excess flour and dip it into the egg, then back to the flour. Set aside and repeat with the other chicken.
Put the chicken into the fryer or air fryer and cook. In the fryer this will take about 5 minutes, in the air fryer, about 30. I like to lightly brush some warm oil on the chicken in the air fryer at about the halfway point. Cook until the outside is crispy and browned and the inside is at 155 degrees.
Build the sandwich - Toast the buns if desired. Spread a thin layer of mayo on the top and bottom bun. Add the chicken next, followed by the blackberry habanero honey. Top with a few slices of the pickled onion, and a few leaves of basil. Serve.