Prep the squash: Cut the kabocha squash in half through the stem and scoop out the seeds. Cut each half in half, then cut into ½-inch-thick slices. Transfer to a large bowl.
2. Step
Cut the ends off the delicata squash, then slice in half lengthwise. Scoop out the seeds, then cut into ½-inch-thick slices. Add to the bowl with the kabocha squash. Season with the salt, white pepper, sesame oil, and ginger and toss to coat.
3. Step
Make the sauce: Melt the butter in a small pot over medium heat. Add the garlic and let sizzle for a minute, until fragrant. Add the gochujang, ketchup, honey, brown sugar, rice vinegar, soy sauce, and sesame oil and whisk to combine. Bring to a simmer and cook for 2–3 minutes, then remove the pot from the heat.
4. Step
In a medium bowl, stir together the potato starch and the panko. Sprinkle over the squash and toss to coat evenly (if the squash pieces do not have an even light white coating, add more potato starch and toss again). Press the panko onto the squash to adhere.
5. Step
Heat a few inches of canola oil in a wok over medium-high heat until the temperature reaches 350°F (180°C). Place a wire rack over a sheet tray.
6. Step
Working in batches to avoid overcrowding the pan, use tongs to carefully lower the squash pieces into the hot oil. Fry for 4–6 minutes, until dark golden brown. Transfer to the wire rack.
7. Step
While the squash is still hot, toss in a large bowl with the sauce until well coated.
8. Step
Garnished with sliced scallions and sesame seeds, then serve.
