Place chopped squash and parsnip in an even layer on a microwave safe plate, and cook on high in the microwave until heated through, but still firm to the touch (5 minutes).
Add 1 tablespoon oil to a large cast-iron (or non-stick) skillet, and warm over medium heat. Cook the sausage, stirring occasionally, until browned and fully cooked through (about 5 minutes). Transfer sausage to a plate and set aside. Wipe the skillet clean.
Return the skillet to a medium-high heat, warm 2 tablespoons olive oil and add the squash and parsnips along with a pinch of salt. Cook, stirring occasionally, until golden on most sides (4 to 5 minutes). You'll want to let the veggies cook undisturbed for 1 - 2 minutes, then toss, stir and repeat. Avoid moving the veggies around in the pan.
Add the onion to the skillet, season with salt and pepper, and cook, stirring occasionally, until tender (about 3 minutes). Stir in the garlic and cook until fragrant (30 seconds). Move the veggies to one half of the skillet. Place remaining tablespoon of oil in the other half of the skillet. Let the oil warm for a moment, then add the sliced kale and a small pinch of salt, stirring to combine. Cook, stirring occasionally, until the greens wilt (2 to 3 minutes). Take the skillet off the heat, stir in the vinegar, and season to taste with additional salt and pepper. Stir in the cooked sausage, and let warm for a moment in the hot skillet.
To serve, spoon 1/4 of the hash in a shallow bowl and top with a scattering of torn parsley leaves. Store additional portions covered in the fridge.