Preheat oven to 350 degrees Fahrenheit.
Line a baking sheet with parchment paper or a silicone mat.
Slice the squash into ½-inch thick half-moons, place in a mixing bowl, and drizzle with olive oil and a pinch of salt to coat so the squash has a nice glossy sheen.
Lay the coated squash in one even layer on the baking sheet and roast in the oven until slightly browned and tender, about 12-15 minutes.
Place the radicchio in a large mixing bowl and coat it with two tablespoons of olive oil, lemon juice, red wine vinegar, salt, and freshly ground black pepper to taste and mix.
Add seasoned radicchio to a serving bowl or platter, add the roasted squash, persimmons, and toasted hazelnuts, and place the burrata on top.
Drizzle a tablespoon of the finishing olive oil on top of the burrata and a pinch of flaky sea salt, and enjoy.