Preheat the oven to 400°F.
Drizzle 1 tablespoon of the avocado oil on both squash halves and place cut-side down on a wire rack set in a sheet pan. Bake for 40 minutes, or until tender. Remove and allow to cool slightly. Turn the halves over, fluff the flesh with a fork and set aside. Turn the oven to low broil and adjust the oven rack.
In a skillet over medium-high heat, heat the remaining 1 tablespoon avocado oil. Add the garlic and sauté for 1 to 2 minutes, or until fragrant. Add the kale and cook for an additional minute.
Add the heavy cream and cream cheese and whisk until combined. Add the Parmesan cheese and season with salt, then transfer the mixture to the squash boats. Top with the breadcrumbs.
Broil under low heat just until the cheese melts and is golden, 5 to 8 minutes. Top with more Parmesan and serve immediately.