Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Cut the squash in half lengthwise and use a spoon to scoop out the seeds and discard. Drizzle with 1 tablespoon olive oil and season with salt and pepper. Place cut-side down on the lined baking sheet and bake until tender, 25 to 30 minutes. Leave the oven on at 400 degrees F.
Heat the butter and 1 tablespoon olive oil in a large skillet over medium-low heat until the butter is melted. Add the breadcrumbs, increase the heat to medium high and cook, stirring constantly, until the breadcrumbs begin to turn golden brown. Stir in the parsley and garlic salt. Transfer to a dish.
Wipe the skillet clean. Heat the remaining 1 tablespoon olive oil over medium heat. Saute the mushrooms and leeks until tender, 5 to 6 minutes. Stir in the kale and garlic and cook until the kale wilts, about 5 minutes. Stir in the rice, currants, soy sauce, honey and vinegar. Season with salt and pepper.
Scoop some of the mixture into the cavity of each acorn squash half and top with the reserved breadcrumbs. Bake until heated through, 25 to 30 minutes.