Pre-heat oven to 425 degrees.
In a small bowl, whisk together ¼ cup plus 2 tablespoons oil, lemon juice, and parsley and sprinkle with salt and pepper.
In a large skillet (cast iron if possible), heat remaining 2 Tbsp olive oil over medium-high heat.
Cook onions and garlic for about 3 minutes, stirring occasionally.
Add squash and carrots to skillet and season with salt and pepper. Transfer skillet to oven and let roast at 425 degrees for 20-25 minutes, until golden. Stir once, halfway through.
Stir kale into squash mixture, with ¼ cup parsley dressing. Return skillet to oven for 7 minutes.
Form four wells in squash mixture and crack eggs into wells. Place skillet back in oven and roast Make 4 wells in vegetables and crack an egg into each. Season eggs with salt. Return to oven and let bake until egg whites are set but yolks remain runny, 4 to 6 minutes.
Serve hash, drizzled with more parsley dressing.