Preheat oven to 400°F (200°C). Drizzle squash with 1 tbsp olive oil, season with salt and pepper. Place cut-side down on a baking sheet and roast for 40-45 minutes.
In a skillet, heat 1 tbsp olive oil. Sauté mushrooms until browned. Add shallots and garlic, cook until fragrant.
Lower heat, add spinach and wilt. Stir in feta, ricotta, oregano, and thyme.
Flip roasted squash boats cut-side up. Scoop out a small amount of flesh if needed. Divide filling between halves.
Top with mozzarella and Parmesan. Bake for 10-15 minutes until cheese is bubbly.
Garnish with fresh thyme and black pepper.