Shred the squash, you'll need around 4-5 medium squash. Blot the shredded squash with paper towels to remove excess moisture. (Alternatively, squeeze in a clean kitchen towel._
In a large bowl stir together the shredded squash, diced onion and egg.
To the bowl add the self-rising flour, grated Parmesan, chopped chives, seasoned salt, garlic powder, cumin, black pepper and cayenne. Stir to combine.
Heat 1 Tbsp vegetable oil and a 1 Tbsp butter in a large nonstick skillet.
Use a Tbsp or a medium ice cream scoop to divide evenly. Scoop the squash mixture, sprinkle with panko bread crumbs, then drop the squash batter crumb side down into the pan. Sprinkle the top side with panko bread crumbs before turning. (Form into approximately 1 1/2-inch-thick patties.)
Fry squash cakes in batches over medium-high heat, cooking until golden brown and cooked through. Around 2-3 minutes per side. Repeat with the remaining squash mixture.
Add additional oil and butter to the pan as needed between batches. Remove fried squash croquettes to a paper towel-lined platter. (You can also keep warm in a preheated 200°F oven on a rimmed baking sheet until serving.)
Serve immediately.