Preheat the oven to 375°F and lightly butter or spray an 8×8-inch baking dish.

Cook the rice according to package directions. You should have 2 cups of cooked wild rice.

In a large skillet, melt the butter with olive oil over medium heat. Add the onion and kale. Cook for 3 minutes, stirring occasionally, until softened. Stir in the garlic, chopped sage, thyme, nutmeg, salt, and pepper; cook for an additional 30 seconds, just until fragrant. Reduce the heat to low, sprinkle in the flour, and whisk to combine. Stir in the Dijon mustard.

Gradually whisk in the milk and vegetable broth until smooth. Stir in the apple cider vinegar and cook for 1 minute, just until slightly thickened.

Remove from the heat. Stir in the cooked wild rice and ¼ cup Parmesan. Combine the cheddar and mozzarella cheeses, then add ½ cup of the cheddar–mozzarella blend and stir to combine.

Transfer the mixture to the prepared baking dish and spread into an even layer. Top with the remaining ½ cup cheddar–mozzarella blend and 2 tablespoons Parmesan. Bake uncovered for 20–25 minutes, until heated through and lightly browned on top.

Let the casserole stand 5 minutes, then serve warm.