Preheat oven to 400° F.
Cut the squash in half lengthwise; use a spoon to remove the seeds and pulp. *See note below about softening squash.
Brush the cut halves with 1 Tablespoon olive oil and sprinkle with 1/4 teaspoon salt and 1/4 teaspoon pepper. Place face down on a rimmed baking sheet lined with parchment paper.
Roast at 400° for 30 - 35 minutes, until fork-tender. Once done, carefully flip squash face up.
Heat 1 Tablespoon olive oil in a large skillet over medium heat. Add chopped shallot and sauté 2-3 minutes, until golden brown and fragrant.
Add sliced almonds and toast 2-3 minutes, until golden brown.
Add baby kale and 1/4 cup broth. Cook 1-2 minutes, stirring regularly.
Add remaining 1/4 cup broth, cooked rice, bacon, dried cranberries, 2 sprigs thyme (leaves), and remaining salt & pepper. Stir in shaved Parmesan.
Divide the filling evenly among the squash. (You will use all of it.) Bake at 400° for 15 minutes. Remove from oven.
In a small bowl, combine melted butter, honey, and leaves from 1 sprig of thyme. Mix well.
Drizzle stuffed squash with honey-thyme butter and garnish with additional Parmesan as desired.