Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with foil or parchment paper.

Brush cut sides of squash with 2 teaspoons oil. Place cut-sides down on the baking sheet.

Bake in the preheated oven until soft, 20 to 25 minutes.

Heat 1 tablespoon oil in a medium pan over medium-high heat. Add turkey sausage. Saute, breaking up into small crumbles, until browned, 2 to 3 minutes. Reduce heat to medium and add celery, onion, garlic, sage, rosemary and thyme. Continue cooking until vegetables are soft, 4 to 5 minutes. Stir in rice, cherries, and parsley until mixture is warmed through, 1 to 2 minutes.

Turn squash halves over so they are cut-side up. Fill with the sausage mixture and top with Parmesan cheese. Return to oven and bake until cheese is melted, 2 to 3 minutes.