Preheat oven to 200°C (400°F). Cut acorn squash in half and remove seeds. Place cut-side up on baking sheet.
Brush squash with olive oil, then season with salt, pepper, and rosemary or thyme. Roast for 30–35 minutes until fork-tender and golden.
Meanwhile, whip together burrata, mascarpone, and lemon zest in a small bowl until smooth and creamy. Set aside.
In a saucepan, gently heat honey with chili flakes and smoked paprika. When warm and bubbling, remove from heat and stir in pistachios. Let cool slightly.
Once squash is roasted and cooled slightly, fill centers with whipped burrata mixture. Top with chili-honey pistachios and fresh herbs.
